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bc",[573,1139,1141,1163],{"className":1140,"ariaHidden":617},[616],[573,1142,1144,1148,1151,1154,1157,1160],{"className":1143},[621],[573,1145],{"className":1146,"style":1147},[625],"height:0.7778em;vertical-align:-0.0833em;",[573,1149,994],{"className":1150},[630,634],[573,1152,1025],{"className":1153},[630,634],[573,1155],{"className":1156,"style":774},[773],[573,1158,603],{"className":1159},[778],[573,1161],{"className":1162,"style":774},[773],[573,1164,1166,1169,1172],{"className":1165},[621],[573,1167],{"className":1168,"style":1037},[625],[573,1170,1062],{"className":1171},[630,634],[573,1173,1091],{"className":1174},[630,634]," teilen.",[564,1177,1178,1179,1342,1343,1371,1372,571,1400,1403],{},"Die Inverse existiert genau dann, wenn ",[573,1180,1182,1221],{"className":1181},[576],[573,1183,1185],{"className":1184},[580],[582,1186,1187],{"xmlns":584},[586,1188,1189,1218],{},[589,1190,1191,1194,1197,1199,1201,1203,1205,1207,1209,1211,1215],{},[595,1192,1193],{},"det",[601,1195,1196],{},"⁡",[595,1198,597],{},[601,1200,735],{},[595,1202,994],{},[595,1204,1025],{},[601,1206,603],{},[595,1208,1062],{},[595,1210,1091],{},[601,1212,1214],{"mathvariant":1213},"normal","≠",[605,1216,1217],{},"0",[609,1219,1220],{"encoding":611},"\\det A = ad - bc \\neq 0",[573,1222,1224,1250,1271,1333],{"className":1223,"ariaHidden":617},[616],[573,1225,1227,1230,1234,1238,1241,1244,1247],{"className":1226},[621],[573,1228],{"className":1229,"style":1037},[625],[573,1231,1193],{"className":1232},[1233],"mop",[573,1235],{"className":1236,"style":1237},[773],"margin-right:0.1667em;",[573,1239,597],{"className":1240},[630,634],[573,1242],{"className":1243,"style":826},[773],[573,1245,735],{"className":1246},[830],[573,1248],{"className":1249,"style":826},[773],[573,1251,1253,1256,1259,1262,1265,1268],{"className":1252},[621],[573,1254],{"className":1255,"style":1147},[625],[573,1257,994],{"className":1258},[630,634],[573,1260,1025],{"className":1261},[630,634],[573,1263],{"className":1264,"style":774},[773],[573,1266,603],{"className":1267},[778],[573,1269],{"className":1270,"style":774},[773],[573,1272,1274,1278,1281,1284,1287,1330],{"className":1273},[621],[573,1275],{"className":1276,"style":1277},[625],"height:0.8889em;vertical-align:-0.1944em;",[573,1279,1062],{"className":1280},[630,634],[573,1282,1091],{"className":1283},[630,634],[573,1285],{"className":1286,"style":826},[773],[573,1288,1290,1323,1327],{"className":1289},[830],[573,1291,1293],{"className":1292},[830],[573,1294,1297],{"className":1295},[630,1296],"vbox",[573,1298,1301],{"className":1299},[1300],"thinbox",[573,1302,1305,1308,1319],{"className":1303},[1304],"rlap",[573,1306],{"className":1307,"style":1277},[625],[573,1309,1312],{"className":1310},[1311],"inner",[573,1313,1315],{"className":1314},[630],[573,1316,1318],{"className":1317},[830],"",[573,1320],{"className":1321},[1322],"fix",[573,1324],{"className":1325},[773,1326],"nobreak",[573,1328,735],{"className":1329},[830],[573,1331],{"className":1332,"style":826},[773],[573,1334,1336,1339],{"className":1335},[621],[573,1337],{"className":1338,"style":964},[625],[573,1340,1217],{"className":1341},[630]," ist. Ist die Determinante ",[573,1344,1346,1359],{"className":1345},[576],[573,1347,1349],{"className":1348},[580],[582,1350,1351],{"xmlns":584},[586,1352,1353,1357],{},[589,1354,1355],{},[605,1356,1217],{},[609,1358,1217],{"encoding":611},[573,1360,1362],{"className":1361,"ariaHidden":617},[616],[573,1363,1365,1368],{"className":1364},[621],[573,1366],{"className":1367,"style":964},[625],[573,1369,1217],{"className":1370},[630],", heißt ",[573,1373,1375,1388],{"className":1374},[576],[573,1376,1378],{"className":1377},[580],[582,1379,1380],{"xmlns":584},[586,1381,1382,1386],{},[589,1383,1384],{},[595,1385,597],{},[609,1387,597],{"encoding":611},[573,1389,1391],{"className":1390,"ariaHidden":617},[616],[573,1392,1394,1397],{"className":1393},[621],[573,1395],{"className":1396,"style":701},[625],[573,1398,597],{"className":1399},[630,634],[568,1401,1402],{},"singulär"," und hat keine Inverse.",[564,1405,1406,1407,1558,1559,1587,1588,1756],{},"Anwendung: Ein Gleichungssystem ",[573,1408,1410,1441],{"className":1409},[576],[573,1411,1413],{"className":1412},[580],[582,1414,1415],{"xmlns":584},[586,1416,1417,1438],{},[589,1418,1419,1421,1430,1432],{},[595,1420,597],{},[1422,1423,1424,1427],"mover",{"accent":617},[595,1425,1426],{},"x",[601,1428,1429],{},"⃗",[601,1431,735],{},[1422,1433,1434,1436],{"accent":617},[595,1435,1062],{},[601,1437,1429],{},[609,1439,1440],{"encoding":611},"A\\vec{x} = \\vec{b}",[573,1442,1444,1514],{"className":1443,"ariaHidden":617},[616],[573,1445,1447,1451,1454,1505,1508,1511],{"className":1446},[621],[573,1448],{"className":1449,"style":1450},[625],"height:0.714em;",[573,1452,597],{"className":1453},[630,634],[573,1455,1458],{"className":1456},[630,1457],"accent",[573,1459,1461],{"className":1460},[642],[573,1462,1464],{"className":1463},[646],[573,1465,1467,1477],{"className":1466,"style":1450},[650],[573,1468,1470,1474],{"style":1469},"top:-3em;",[573,1471],{"className":1472,"style":1473},[657],"height:3em;",[573,1475,1426],{"className":1476},[630,634],[573,1478,1479,1482],{"style":1469},[573,1480],{"className":1481,"style":1473},[657],[573,1483,1487],{"className":1484,"style":1486},[1485],"accent-body","left:-0.2077em;",[573,1488,1492],{"className":1489,"style":1491},[1490],"overlay","height:0.714em;width:0.471em;",[1493,1494,1501],"svg",{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[1502,1503],"path",{"d":1504},"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z",[573,1506],{"className":1507,"style":826},[773],[573,1509,735],{"className":1510},[830],[573,1512],{"className":1513,"style":826},[773],[573,1515,1517,1521],{"className":1516},[621],[573,1518],{"className":1519,"style":1520},[625],"height:0.9774em;",[573,1522,1524],{"className":1523},[630,1457],[573,1525,1527],{"className":1526},[642],[573,1528,1530],{"className":1529},[646],[573,1531,1533,1541],{"className":1532,"style":1520},[650],[573,1534,1535,1538],{"style":1469},[573,1536],{"className":1537,"style":1473},[657],[573,1539,1062],{"className":1540},[630,634],[573,1542,1544,1547],{"style":1543},"top:-3.2634em;",[573,1545],{"className":1546,"style":1473},[657],[573,1548,1551],{"className":1549,"style":1550},[1485],"left:-0.2355em;",[573,1552,1554],{"className":1553,"style":1491},[1490],[1493,1555,1556],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,1557],{"d":1504}," mit invertierbarem ",[573,1560,1562,1575],{"className":1561},[576],[573,1563,1565],{"className":1564},[580],[582,1566,1567],{"xmlns":584},[586,1568,1569,1573],{},[589,1570,1571],{},[595,1572,597],{},[609,1574,597],{"encoding":611},[573,1576,1578],{"className":1577,"ariaHidden":617},[616],[573,1579,1581,1584],{"className":1580},[621],[573,1582],{"className":1583,"style":701},[625],[573,1585,597],{"className":1586},[630,634]," hat die eindeutige Lösung ",[573,1589,1591,1627],{"className":1590},[576],[573,1592,1594],{"className":1593},[580],[582,1595,1596],{"xmlns":584},[586,1597,1598,1624],{},[589,1599,1600,1606,1608,1618],{},[1422,1601,1602,1604],{"accent":617},[595,1603,1426],{},[601,1605,1429],{},[601,1607,735],{},[592,1609,1610,1612],{},[595,1611,597],{},[589,1613,1614,1616],{},[601,1615,603],{},[605,1617,607],{},[1422,1619,1620,1622],{"accent":617},[595,1621,1062],{},[601,1623,1429],{},[609,1625,1626],{"encoding":611},"\\vec{x} = A^{-1}\\vec{b}",[573,1628,1630,1680],{"className":1629,"ariaHidden":617},[616],[573,1631,1633,1636,1671,1674,1677],{"className":1632},[621],[573,1634],{"className":1635,"style":1450},[625],[573,1637,1639],{"className":1638},[630,1457],[573,1640,1642],{"className":1641},[642],[573,1643,1645],{"className":1644},[646],[573,1646,1648,1656],{"className":1647,"style":1450},[650],[573,1649,1650,1653],{"style":1469},[573,1651],{"className":1652,"style":1473},[657],[573,1654,1426],{"className":1655},[630,634],[573,1657,1658,1661],{"style":1469},[573,1659],{"className":1660,"style":1473},[657],[573,1662,1664],{"className":1663,"style":1486},[1485],[573,1665,1667],{"className":1666,"style":1491},[1490],[1493,1668,1669],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,1670],{"d":1504},[573,1672],{"className":1673,"style":826},[773],[573,1675,735],{"className":1676},[830],[573,1678],{"className":1679,"style":826},[773],[573,1681,1683,1686,1721],{"className":1682},[621],[573,1684],{"className":1685,"style":1520},[625],[573,1687,1689,1692],{"className":1688},[630],[573,1690,597],{"className":1691},[630,634],[573,1693,1695],{"className":1694},[638],[573,1696,1698],{"className":1697},[642],[573,1699,1701],{"className":1700},[646],[573,1702,1704],{"className":1703,"style":626},[650],[573,1705,1706,1709],{"style":653},[573,1707],{"className":1708,"style":658},[657],[573,1710,1712],{"className":1711},[662,663,664,665],[573,1713,1715,1718],{"className":1714},[630,665],[573,1716,603],{"className":1717},[630,665],[573,1719,607],{"className":1720},[630,665],[573,1722,1724],{"className":1723},[630,1457],[573,1725,1727],{"className":1726},[642],[573,1728,1730],{"className":1729},[646],[573,1731,1733,1741],{"className":1732,"style":1520},[650],[573,1734,1735,1738],{"style":1469},[573,1736],{"className":1737,"style":1473},[657],[573,1739,1062],{"className":1740},[630,634],[573,1742,1743,1746],{"style":1543},[573,1744],{"className":1745,"style":1473},[657],[573,1747,1749],{"className":1748,"style":1550},[1485],[573,1750,1752],{"className":1751,"style":1491},[1490],[1493,1753,1754],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,1755],{"d":1504},". Für größere Matrizen bestimmt man die Inverse meist mit dem Gauß-Jordan-Verfahren.",[559,1758,1760],{"id":1759},"beispiele","Beispiele",[564,1762,1763,1764,1992,1993,2100],{},"Für ",[573,1765,1767,1831],{"className":1766},[576],[573,1768,1770],{"className":1769},[580],[582,1771,1772],{"xmlns":584},[586,1773,1774,1828],{},[589,1775,1776,1778,1780],{},[595,1777,597],{},[601,1779,735],{},[589,1781,1782,1785,1825],{},[601,1783,1784],{"fence":617},"(",[1786,1787,1791,1810],"mtable",{"rowspacing":1788,"columnalign":1789,"columnspacing":1790},"0.16em","center center","1em",[1792,1793,1794,1804],"mtr",{},[1795,1796,1797],"mtd",{},[1798,1799,1801],"mstyle",{"scriptlevel":1217,"displaystyle":1800},"false",[605,1802,1803],{},"3",[1795,1805,1806],{},[1798,1807,1808],{"scriptlevel":1217,"displaystyle":1800},[605,1809,927],{},[1792,1811,1812,1818],{},[1795,1813,1814],{},[1798,1815,1816],{"scriptlevel":1217,"displaystyle":1800},[605,1817,607],{},[1795,1819,1820],{},[1798,1821,1822],{"scriptlevel":1217,"displaystyle":1800},[605,1823,1824],{},"4",[601,1826,1827],{"fence":617},")",[609,1829,1830],{"encoding":611},"A = \\begin{pmatrix} 3 & 2 \\\\ 1 & 4 \\end{pmatrix}",[573,1832,1834,1852],{"className":1833,"ariaHidden":617},[616],[573,1835,1837,1840,1843,1846,1849],{"className":1836},[621],[573,1838],{"className":1839,"style":701},[625],[573,1841,597],{"className":1842},[630,634],[573,1844],{"className":1845,"style":826},[773],[573,1847,735],{"className":1848},[830],[573,1850],{"className":1851,"style":826},[773],[573,1853,1855,1859],{"className":1854},[621],[573,1856],{"className":1857,"style":1858},[625],"height:2.4em;vertical-align:-0.95em;",[573,1860,1863,1873,1985],{"className":1861},[1862],"minner",[573,1864,1869],{"className":1865,"style":1868},[1866,1867],"mopen","delimcenter","top:0em;",[573,1870,1784],{"className":1871},[1872,664],"delimsizing",[573,1874,1876],{"className":1875},[630],[573,1877,1879,1932,1937,1940],{"className":1878},[1786],[573,1880,1883],{"className":1881},[1882],"col-align-c",[573,1884,1887,1923],{"className":1885},[642,1886],"vlist-t2",[573,1888,1890,1918],{"className":1889},[646],[573,1891,1894,1906],{"className":1892,"style":1893},[650],"height:1.45em;",[573,1895,1897,1900],{"style":1896},"top:-3.61em;",[573,1898],{"className":1899,"style":1473},[657],[573,1901,1903],{"className":1902},[630],[573,1904,1803],{"className":1905},[630],[573,1907,1909,1912],{"style":1908},"top:-2.41em;",[573,1910],{"className":1911,"style":1473},[657],[573,1913,1915],{"className":1914},[630],[573,1916,607],{"className":1917},[630],[573,1919,1922],{"className":1920},[1921],"vlist-s","​",[573,1924,1926],{"className":1925},[646],[573,1927,1930],{"className":1928,"style":1929},[650],"height:0.95em;",[573,1931],{},[573,1933],{"className":1934,"style":1936},[1935],"arraycolsep","width:0.5em;",[573,1938],{"className":1939,"style":1936},[1935],[573,1941,1943],{"className":1942},[1882],[573,1944,1946,1977],{"className":1945},[642,1886],[573,1947,1949,1974],{"className":1948},[646],[573,1950,1952,1963],{"className":1951,"style":1893},[650],[573,1953,1954,1957],{"style":1896},[573,1955],{"className":1956,"style":1473},[657],[573,1958,1960],{"className":1959},[630],[573,1961,927],{"className":1962},[630],[573,1964,1965,1968],{"style":1908},[573,1966],{"className":1967,"style":1473},[657],[573,1969,1971],{"className":1970},[630],[573,1972,1824],{"className":1973},[630],[573,1975,1922],{"className":1976},[1921],[573,1978,1980],{"className":1979},[646],[573,1981,1983],{"className":1982,"style":1929},[650],[573,1984],{},[573,1986,1989],{"className":1987,"style":1868},[1988,1867],"mclose",[573,1990,1827],{"className":1991},[1872,664]," ist ",[573,1994,1996,2028],{"className":1995},[576],[573,1997,1999],{"className":1998},[580],[582,2000,2001],{"xmlns":584},[586,2002,2003,2025],{},[589,2004,2005,2007,2009,2011,2013,2016,2018,2020,2022],{},[595,2006,1193],{},[601,2008,1196],{},[595,2010,597],{},[601,2012,735],{},[605,2014,2015],{},"12",[601,2017,603],{},[605,2019,927],{},[601,2021,735],{},[605,2023,2024],{},"10",[609,2026,2027],{"encoding":611},"\\det A = 12 - 2 = 10",[573,2029,2031,2055,2073,2091],{"className":2030,"ariaHidden":617},[616],[573,2032,2034,2037,2040,2043,2046,2049,2052],{"className":2033},[621],[573,2035],{"className":2036,"style":1037},[625],[573,2038,1193],{"className":2039},[1233],[573,2041],{"className":2042,"style":1237},[773],[573,2044,597],{"className":2045},[630,634],[573,2047],{"className":2048,"style":826},[773],[573,2050,735],{"className":2051},[830],[573,2053],{"className":2054,"style":826},[773],[573,2056,2058,2061,2064,2067,2070],{"className":2057},[621],[573,2059],{"className":2060,"style":945},[625],[573,2062,2015],{"className":2063},[630],[573,2065],{"className":2066,"style":774},[773],[573,2068,603],{"className":2069},[778],[573,2071],{"className":2072,"style":774},[773],[573,2074,2076,2079,2082,2085,2088],{"className":2075},[621],[573,2077],{"className":2078,"style":964},[625],[573,2080,927],{"className":2081},[630],[573,2083],{"className":2084,"style":826},[773],[573,2086,735],{"className":2087},[830],[573,2089],{"className":2090,"style":826},[773],[573,2092,2094,2097],{"className":2093},[621],[573,2095],{"className":2096,"style":964},[625],[573,2098,2024],{"className":2099},[630],":",[573,2102,2105],{"className":2103},[2104],"katex-display",[573,2106,2108,2234],{"className":2107},[576],[573,2109,2111],{"className":2110},[580],[582,2112,2114],{"xmlns":584,"display":2113},"block",[586,2115,2116,2231],{},[589,2117,2118,2128,2130,2137,2181,2183],{},[592,2119,2120,2122],{},[595,2121,597],{},[589,2123,2124,2126],{},[601,2125,603],{},[605,2127,607],{},[601,2129,735],{},[2131,2132,2133,2135],"mfrac",{},[605,2134,607],{},[605,2136,2024],{},[589,2138,2139,2141,2179],{},[601,2140,1784],{"fence":617},[1786,2142,2143,2161],{"rowspacing":1788,"columnalign":1789,"columnspacing":1790},[1792,2144,2145,2151],{},[1795,2146,2147],{},[1798,2148,2149],{"scriptlevel":1217,"displaystyle":1800},[605,2150,1824],{},[1795,2152,2153],{},[1798,2154,2155],{"scriptlevel":1217,"displaystyle":1800},[589,2156,2157,2159],{},[601,2158,603],{},[605,2160,927],{},[1792,2162,2163,2173],{},[1795,2164,2165],{},[1798,2166,2167],{"scriptlevel":1217,"displaystyle":1800},[589,2168,2169,2171],{},[601,2170,603],{},[605,2172,607],{},[1795,2174,2175],{},[1798,2176,2177],{"scriptlevel":1217,"displaystyle":1800},[605,2178,1803],{},[601,2180,1827],{"fence":617},[601,2182,735],{},[589,2184,2185,2187,2229],{},[601,2186,1784],{"fence":617},[1786,2188,2189,2209],{"rowspacing":1788,"columnalign":1789,"columnspacing":1790},[1792,2190,2191,2198],{},[1795,2192,2193],{},[1798,2194,2195],{"scriptlevel":1217,"displaystyle":1800},[605,2196,2197],{},"0,4",[1795,2199,2200],{},[1798,2201,2202],{"scriptlevel":1217,"displaystyle":1800},[589,2203,2204,2206],{},[601,2205,603],{},[605,2207,2208],{},"0,2",[1792,2210,2211,2222],{},[1795,2212,2213],{},[1798,2214,2215],{"scriptlevel":1217,"displaystyle":1800},[589,2216,2217,2219],{},[601,2218,603],{},[605,2220,2221],{},"0,1",[1795,2223,2224],{},[1798,2225,2226],{"scriptlevel":1217,"displaystyle":1800},[605,2227,2228],{},"0,3",[601,2230,1827],{"fence":617},[609,2232,2233],{"encoding":611},"A^{-1} = \\frac{1}{10} \\begin{pmatrix} 4 & -2 \\\\ -1 & 3 \\end{pmatrix} = \\begin{pmatrix} 0{,}4 & -0{,}2 \\\\ -0{,}1 & 0{,}3 \\end{pmatrix}",[573,2235,2237,2289,2500],{"className":2236,"ariaHidden":617},[616],[573,2238,2240,2244,2280,2283,2286],{"className":2239},[621],[573,2241],{"className":2242,"style":2243},[625],"height:0.8641em;",[573,2245,2247,2250],{"className":2246},[630],[573,2248,597],{"className":2249},[630,634],[573,2251,2253],{"className":2252},[638],[573,2254,2256],{"className":2255},[642],[573,2257,2259],{"className":2258},[646],[573,2260,2262],{"className":2261,"style":2243},[650],[573,2263,2265,2268],{"style":2264},"top:-3.113em;margin-right:0.05em;",[573,2266],{"className":2267,"style":658},[657],[573,2269,2271],{"className":2270},[662,663,664,665],[573,2272,2274,2277],{"className":2273},[630,665],[573,2275,603],{"className":2276},[630,665],[573,2278,607],{"className":2279},[630,665],[573,2281],{"className":2282,"style":826},[773],[573,2284,735],{"className":2285},[830],[573,2287],{"className":2288,"style":826},[773],[573,2290,2292,2295,2365,2368,2491,2494,2497],{"className":2291},[621],[573,2293],{"className":2294,"style":1858},[625],[573,2296,2298,2302,2362],{"className":2297},[630],[573,2299],{"className":2300},[1866,2301],"nulldelimiter",[573,2303,2305],{"className":2304},[2131],[573,2306,2308,2353],{"className":2307},[642,1886],[573,2309,2311,2350],{"className":2310},[646],[573,2312,2315,2327,2338],{"className":2313,"style":2314},[650],"height:1.3214em;",[573,2316,2318,2321],{"style":2317},"top:-2.314em;",[573,2319],{"className":2320,"style":1473},[657],[573,2322,2324],{"className":2323},[630],[573,2325,2024],{"className":2326},[630],[573,2328,2330,2333],{"style":2329},"top:-3.23em;",[573,2331],{"className":2332,"style":1473},[657],[573,2334],{"className":2335,"style":2337},[2336],"frac-line","border-bottom-width:0.04em;",[573,2339,2341,2344],{"style":2340},"top:-3.677em;",[573,2342],{"className":2343,"style":1473},[657],[573,2345,2347],{"className":2346},[630],[573,2348,607],{"className":2349},[630],[573,2351,1922],{"className":2352},[1921],[573,2354,2356],{"className":2355},[646],[573,2357,2360],{"className":2358,"style":2359},[650],"height:0.686em;",[573,2361],{},[573,2363],{"className":2364},[1988,2301],[573,2366],{"className":2367,"style":1237},[773],[573,2369,2371,2377,2485],{"className":2370},[1862],[573,2372,2374],{"className":2373,"style":1868},[1866,1867],[573,2375,1784],{"className":2376},[1872,664],[573,2378,2380],{"className":2379},[630],[573,2381,2383,2431,2434,2437],{"className":2382},[1786],[573,2384,2386],{"className":2385},[1882],[573,2387,2389,2423],{"className":2388},[642,1886],[573,2390,2392,2420],{"className":2391},[646],[573,2393,2395,2406],{"className":2394,"style":1893},[650],[573,2396,2397,2400],{"style":1896},[573,2398],{"className":2399,"style":1473},[657],[573,2401,2403],{"className":2402},[630],[573,2404,1824],{"className":2405},[630],[573,2407,2408,2411],{"style":1908},[573,2409],{"className":2410,"style":1473},[657],[573,2412,2414,2417],{"className":2413},[630],[573,2415,603],{"className":2416},[630],[573,2418,607],{"className":2419},[630],[573,2421,1922],{"className":2422},[1921],[573,2424,2426],{"className":2425},[646],[573,2427,2429],{"className":2428,"style":1929},[650],[573,2430],{},[573,2432],{"className":2433,"style":1936},[1935],[573,2435],{"className":2436,"style":1936},[1935],[573,2438,2440],{"className":2439},[1882],[573,2441,2443,2477],{"className":2442},[642,1886],[573,2444,2446,2474],{"className":2445},[646],[573,2447,2449,2463],{"className":2448,"style":1893},[650],[573,2450,2451,2454],{"style":1896},[573,2452],{"className":2453,"style":1473},[657],[573,2455,2457,2460],{"className":2456},[630],[573,2458,603],{"className":2459},[630],[573,2461,927],{"className":2462},[630],[573,2464,2465,2468],{"style":1908},[573,2466],{"className":2467,"style":1473},[657],[573,2469,2471],{"className":2470},[630],[573,2472,1803],{"className":2473},[630],[573,2475,1922],{"className":2476},[1921],[573,2478,2480],{"className":2479},[646],[573,2481,2483],{"className":2482,"style":1929},[650],[573,2484],{},[573,2486,2488],{"className":2487,"style":1868},[1988,1867],[573,2489,1827],{"className":2490},[1872,664],[573,2492],{"className":2493,"style":826},[773],[573,2495,735],{"className":2496},[830],[573,2498],{"className":2499,"style":826},[773],[573,2501,2503,2506],{"className":2502},[621],[573,2504],{"className":2505,"style":1858},[625],[573,2507,2509,2515,2661],{"className":2508},[1862],[573,2510,2512],{"className":2511,"style":1868},[1866,1867],[573,2513,1784],{"className":2514},[1872,664],[573,2516,2518],{"className":2517},[630],[573,2519,2521,2589,2592,2595],{"className":2520},[1786],[573,2522,2524],{"className":2523},[1882],[573,2525,2527,2581],{"className":2526},[642,1886],[573,2528,2530,2578],{"className":2529},[646],[573,2531,2533,2555],{"className":2532,"style":1893},[650],[573,2534,2535,2538],{"style":1896},[573,2536],{"className":2537,"style":1473},[657],[573,2539,2541,2544,2552],{"className":2540},[630],[573,2542,1217],{"className":2543},[630],[573,2545,2547],{"className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\\cdot A^{-1} = \\begin{pmatrix} 1{,}2 - 0{,}2 & -0{,}6 + 0{,}6 \\\\ 0{,}4 - 0{,}4 & -0{,}2 + 1{,}2 \\end{pmatrix} = \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 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Gleichungssystem ",[573,3264,3266,3294],{"className":3265},[576],[573,3267,3269],{"className":3268},[580],[582,3270,3271],{"xmlns":584},[586,3272,3273,3291],{},[589,3274,3275,3277,3279,3281,3283,3286,3288],{},[605,3276,1803],{},[595,3278,1426],{},[601,3280,2732],{},[605,3282,927],{},[595,3284,3285],{},"y",[601,3287,735],{},[605,3289,3290],{},"8",[609,3292,3293],{"encoding":611},"3x + 2y = 8",[573,3295,3297,3318,3341],{"className":3296,"ariaHidden":617},[616],[573,3298,3300,3303,3306,3309,3312,3315],{"className":3299},[621],[573,3301],{"className":3302,"style":945},[625],[573,3304,1803],{"className":3305},[630],[573,3307,1426],{"className":3308},[630,634],[573,3310],{"className":3311,"style":774},[773],[573,3313,2732],{"className":3314},[778],[573,3316],{"className":3317,"style":774},[773],[573,3319,3321,3325,3328,3332,3335,3338],{"className":3320},[621],[573,3322],{"className":3323,"style":3324},[625],"height:0.8389em;vertical-align:-0.1944em;",[573,3326,927],{"className":3327},[630],[573,3329,3285],{"className":3330,"style":3331},[630,634],"margin-right:0.0359em;",[573,3333],{"className":3334,"style":826},[773],[573,3336,735],{"className":3337},[830],[573,3339],{"className":3340,"style":826},[773],[573,3342,3344,3347],{"className":3343},[621],[573,3345],{"className":3346,"style":964},[625],[573,3348,3290],{"className":3349},[630],", ",[573,3352,3354,3378],{"className":3353},[576],[573,3355,3357],{"className":3356},[580],[582,3358,3359],{"xmlns":584},[586,3360,3361,3375],{},[589,3362,3363,3365,3367,3369,3371,3373],{},[595,3364,1426],{},[601,3366,2732],{},[605,3368,1824],{},[595,3370,3285],{},[601,3372,735],{},[605,3374,3044],{},[609,3376,3377],{"encoding":611},"x + 4y = 6",[573,3379,3381,3400,3421],{"className":3380,"ariaHidden":617},[616],[573,3382,3384,3388,3391,3394,3397],{"className":3383},[621],[573,3385],{"className":3386,"style":3387},[625],"height:0.6667em;vertical-align:-0.0833em;",[573,3389,1426],{"className":3390},[630,634],[573,3392],{"className":3393,"style":774},[773],[573,3395,2732],{"className":3396},[778],[573,3398],{"className":3399,"style":774},[773],[573,3401,3403,3406,3409,3412,3415,3418],{"className":3402},[621],[573,3404],{"className":3405,"style":3324},[625],[573,3407,1824],{"className":3408},[630],[573,3410,3285],{"className":3411,"style":3331},[630,634],[573,3413],{"className":3414,"style":826},[773],[573,3416,735],{"className":3417},[830],[573,3419],{"className":3420,"style":826},[773],[573,3422,3424,3427],{"className":3423},[621],[573,3425],{"className":3426,"style":964},[625],[573,3428,3044],{"className":3429},[630]," hat diese Koeffizientenmatrix. Die Lösung ist",[573,3432,3434],{"className":3433},[2104],[573,3435,3437,3592],{"className":3436},[576],[573,3438,3440],{"className":3439},[580],[582,3441,3442],{"xmlns":584,"display":2113},[586,3443,3444,3589],{},[589,3445,3446,3471,3473,3483,3507,3509,3563,3565],{},[589,3447,3448,3450,3469],{},[601,3449,1784],{"fence":617},[1786,3451,3453,3461],{"rowspacing":1788,"columnalign":3452,"columnspacing":1790},"center",[1792,3454,3455],{},[1795,3456,3457],{},[1798,3458,3459],{"scriptlevel":1217,"displaystyle":1800},[595,3460,1426],{},[1792,3462,3463],{},[1795,3464,3465],{},[1798,3466,3467],{"scriptlevel":1217,"displaystyle":1800},[595,3468,3285],{},[601,3470,1827],{"fence":617},[601,3472,735],{},[592,3474,3475,3477],{},[595,3476,597],{},[589,3478,3479,3481],{},[601,3480,603],{},[605,3482,607],{},[589,3484,3485,3487,3505],{},[601,3486,1784],{"fence":617},[1786,3488,3489,3497],{"rowspacing":1788,"columnalign":3452,"columnspacing":1790},[1792,3490,3491],{},[1795,3492,3493],{},[1798,3494,3495],{"scriptlevel":1217,"displaystyle":1800},[605,3496,3290],{},[1792,3498,3499],{},[1795,3500,3501],{},[1798,3502,3503],{"scriptlevel":1217,"displaystyle":1800},[605,3504,3044],{},[601,3506,1827],{"fence":617},[601,3508,735],{},[589,3510,3511,3513,3561],{},[601,3512,1784],{"fence":617},[1786,3514,3515,3537],{"rowspacing":1788,"columnalign":3452,"columnspacing":1790},[1792,3516,3517],{},[1795,3518,3519],{},[1798,3520,3521],{"scriptlevel":1217,"displaystyle":1800},[589,3522,3523,3525,3527,3529,3531,3533,3535],{},[605,3524,2197],{},[601,3526,722],{},[605,3528,3290],{},[601,3530,603],{},[605,3532,2208],{},[601,3534,722],{},[605,3536,3044],{},[1792,3538,3539],{},[1795,3540,3541],{},[1798,3542,3543],{"scriptlevel":1217,"displaystyle":1800},[589,3544,3545,3547,3549,3551,3553,3555,3557,3559],{},[601,3546,603],{},[605,3548,2221],{},[601,3550,722],{},[605,3552,3290],{},[601,3554,2732],{},[605,3556,2228],{},[601,3558,722],{},[605,3560,3044],{},[601,3562,1827],{"fence":617},[601,3564,735],{},[589,3566,3567,3569,3587],{},[601,3568,1784],{"fence":617},[1786,3570,3571,3579],{"rowspacing":1788,"columnalign":3452,"columnspacing":1790},[1792,3572,3573],{},[1795,3574,3575],{},[1798,3576,3577],{"scriptlevel":1217,"displaystyle":1800},[605,3578,927],{},[1792,3580,3581],{},[1795,3582,3583],{},[1798,3584,3585],{"scriptlevel":1217,"displaystyle":1800},[605,3586,607],{},[601,3588,1827],{"fence":617},[609,3590,3591],{"encoding":611},"\\begin{pmatrix} x \\\\ y \\end{pmatrix} = A^{-1} \\begin{pmatrix} 8 \\\\ 6 \\end{pmatrix} = \\begin{pmatrix} 0{,}4 \\cdot 8 - 0{,}2 \\cdot 6 \\\\ -0{,}1 \\cdot 8 + 0{,}3 \\cdot 6 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix}",[573,3593,3595,3676,3795,3987],{"className":3594,"ariaHidden":617},[616],[573,3596,3598,3601,3667,3670,3673],{"className":3597},[621],[573,3599],{"className":3600,"style":1858},[625],[573,3602,3604,3610,3661],{"className":3603},[1862],[573,3605,3607],{"className":3606,"style":1868},[1866,1867],[573,3608,1784],{"className":3609},[1872,664],[573,3611,3613],{"className":3612},[630],[573,3614,3616],{"className":3615},[1786],[573,3617,3619],{"className":3618},[1882],[573,3620,3622,3653],{"className":3621},[642,1886],[573,3623,3625,3650],{"className":3624},[646],[573,3626,3628,3639],{"className":3627,"style":1893},[650],[573,3629,3630,3633],{"style":1896},[573,3631],{"className":3632,"style":1473},[657],[573,3634,3636],{"className":3635},[630],[573,3637,1426],{"className":3638},[630,634],[573,3640,3641,3644],{"style":1908},[573,3642],{"className":3643,"style":1473},[657],[573,3645,3647],{"className":3646},[630],[573,3648,3285],{"className":3649,"style":3331},[630,634],[573,3651,1922],{"className":3652},[1921],[573,3654,3656],{"className":3655},[646],[573,3657,3659],{"className":3658,"style":1929},[650],[573,3660],{},[573,3662,3664],{"className":3663,"style":1868},[1988,1867],[573,3665,1827],{"className":3666},[1872,664],[573,3668],{"className":3669,"style":826},[773],[573,3671,735],{"className":3672},[830],[573,3674],{"className":3675,"style":826},[773],[573,3677,3679,3682,3717,3720,3786,3789,3792],{"className":3678},[621],[573,3680],{"className":3681,"style":1858},[625],[573,3683,3685,3688],{"className":3684},[630],[573,3686,597],{"className":3687},[630,634],[573,3689,3691],{"className":3690},[638],[573,3692,3694],{"className":3693},[642],[573,3695,3697],{"className":3696},[646],[573,3698,3700],{"className":3699,"style":2243},[650],[573,3701,3702,3705],{"style":2264},[573,3703],{"className":3704,"style":658},[657],[573,3706,3708],{"className":3707},[662,663,664,665],[573,3709,3711,3714],{"className":3710},[630,665],[573,3712,603],{"className":3713},[630,665],[573,3715,607],{"className":3716},[630,665],[573,3718],{"className":3719,"style":1237},[773],[573,3721,3723,3729,3780],{"className":3722},[1862],[573,3724,3726],{"className":3725,"style":1868},[1866,1867],[573,3727,1784],{"className":3728},[1872,664],[573,3730,3732],{"className":3731},[630],[573,3733,3735],{"className":3734},[1786],[573,3736,3738],{"className":3737},[1882],[573,3739,3741,3772],{"className":3740},[642,1886],[573,3742,3744,3769],{"className":3743},[646],[573,3745,3747,3758],{"className":3746,"style":1893},[650],[573,3748,3749,3752],{"style":1896},[573,3750],{"className":3751,"style":1473},[657],[573,3753,3755],{"className":3754},[630],[573,3756,3290],{"className":3757},[630],[573,3759,3760,3763],{"style":1908},[573,3761],{"className":3762,"style":1473},[657],[573,3764,3766],{"className":3765},[630],[573,3767,3044],{"className":3768},[630],[573,3770,1922],{"className":3771},[1921],[573,3773,3775],{"className":3774},[646],[573,3776,3778],{"className":3777,"style":1929},[650],[573,3779],{},[573,3781,3783],{"className":3782,"style":1868},[1988,1867],[573,3784,1827],{"className":3785},[1872,664],[573,3787],{"className":3788,"style":826},[773],[573,3790,735],{"className":3791},[830],[573,3793],{"className":3794,"style":826},[773],[573,3796,3798,3801,3978,3981,3984],{"className":3797},[621],[573,3799],{"className":3800,"style":1858},[625],[573,3802,3804,3810,3972],{"className":3803},[1862],[573,3805,3807],{"className":3806,"style":1868},[1866,1867],[573,3808,1784],{"className":3809},[1872,664],[573,3811,3813],{"className":3812},[630],[573,3814,3816],{"className":3815},[1786],[573,3817,3819],{"className":3818},[1882],[573,3820,3822,3964],{"className":3821},[642,1886],[573,3823,3825,3961],{"className":3824},[646],[573,3826,3828,3893],{"className":3827,"style":1893},[650],[573,3829,3830,3833],{"style":1896},[573,3831],{"className":3832,"style":1473},[657],[573,3834,3836,3839,3845,3848,3851,3854,3857,3860,3863,3866,3869,3872,3878,3881,3884,3887,3890],{"className":3835},[630],[573,3837,1217],{"className":3838},[630],[573,3840,3842],{"className":3841},[630],[573,3843,2551],{"className":3844},[2550],[573,3846,1824],{"className":3847},[630],[573,3849],{"className":3850,"style":774},[773],[573,3852,722],{"className":3853},[778],[573,3855],{"className":3856,"style":774},[773],[573,3858,3290],{"className":3859},[630],[573,3861],{"className":3862,"style":774},[773],[573,3864,603],{"className":3865},[778],[573,3867],{"className":3868,"style":774},[773],[573,3870,1217],{"className":3871},[630],[573,3873,3875],{"className":3874},[630],[573,3876,2551],{"className":3877},[2550],[573,3879,927],{"className":3880},[630],[573,3882],{"className":3883,"style":774},[773],[573,3885,722],{"className":3886},[778],[573,3888],{"className":3889,"style":774},[773],[573,3891,3044],{"className":3892},[630],[573,3894,3895,3898],{"style":1908},[573,3896],{"className":3897,"style":1473},[657],[573,3899,3901,3904,3907,3913,3916,3919,3922,3925,3928,3931,3934,3937,3940,3946,3949,3952,3955,3958],{"className":3900},[630],[573,3902,603],{"className":3903},[630],[573,3905,1217],{"className":3906},[630],[573,3908,3910],{"className":3909},[630],[573,3911,2551],{"className":3912},[2550],[573,3914,607],{"className":3915},[630],[573,3917],{"className":3918,"style":774},[773],[573,3920,722],{"className":3921},[778],[573,3923],{"className":3924,"style":774},[773],[573,3926,3290],{"className":3927},[630],[573,3929],{"className":3930,"style":774},[773],[573,3932,2732],{"className":3933},[778],[573,3935],{"className":3936,"style":774},[773],[573,3938,1217],{"className":3939},[630],[573,3941,3943],{"className":3942},[630],[573,3944,2551],{"className":3945},[2550],[573,3947,1803],{"className":3948},[630],[573,3950],{"className":3951,"style":774},[773],[573,3953,722],{"className":3954},[778],[573,3956],{"className":3957,"style":774},[773],[573,3959,3044],{"className":3960},[630],[573,3962,1922],{"className":3963},[1921],[573,3965,3967],{"className":3966},[646],[573,3968,3970],{"className":3969,"style":1929},[650],[573,3971],{},[573,3973,3975],{"className":3974,"style":1868},[1988,1867],[573,3976,1827],{"className":3977},[1872,664],[573,3979],{"className":3980,"style":826},[773],[573,3982,735],{"className":3983},[830],[573,3985],{"className":3986,"style":826},[773],[573,3988,3990,3993],{"className":3989},[621],[573,3991],{"className":3992,"style":1858},[625],[573,3994,3996,4002,4053],{"className":3995},[1862],[573,3997,3999],{"className":3998,"style":1868},[1866,1867],[573,4000,1784],{"className":4001},[1872,664],[573,4003,4005],{"className":4004},[630],[573,4006,4008],{"className":4007},[1786],[573,4009,4011],{"className":4010},[1882],[573,4012,4014,4045],{"className":4013},[642,1886],[573,4015,4017,4042],{"className":4016},[646],[573,4018,4020,4031],{"className":4019,"style":1893},[650],[573,4021,4022,4025],{"style":1896},[573,4023],{"className":4024,"style":1473},[657],[573,4026,4028],{"className":4027},[630],[573,4029,927],{"className":4030},[630],[573,4032,4033,4036],{"style":1908},[573,4034],{"className":4035,"style":1473},[657],[573,4037,4039],{"className":4038},[630],[573,4040,607],{"className":4041},[630],[573,4043,1922],{"className":4044},[1921],[573,4046,4048],{"className":4047},[646],[573,4049,4051],{"className":4050,"style":1929},[650],[573,4052],{},[573,4054,4056],{"className":4055,"style":1868},[1988,1867],[573,4057,1827],{"className":4058},[1872,664],[564,4060,2669,4061,1010,4178,3259],{},[573,4062,4064,4094],{"className":4063},[576],[573,4065,4067],{"className":4066},[580],[582,4068,4069],{"xmlns":584},[586,4070,4071,4091],{},[589,4072,4073,4075,4077,4079,4081,4083,4085,4087,4089],{},[605,4074,1803],{},[601,4076,722],{},[605,4078,927],{},[601,4080,2732],{},[605,4082,927],{},[601,4084,722],{},[605,4086,607],{},[601,4088,735],{},[605,4090,3290],{},[609,4092,4093],{"encoding":611},"3 \\cdot 2 + 2 \\cdot 1 = 8",[573,4095,4097,4115,4133,4151,4169],{"className":4096,"ariaHidden":617},[616],[573,4098,4100,4103,4106,4109,4112],{"className":4099},[621],[573,4101],{"className":4102,"style":964},[625],[573,4104,1803],{"className":4105},[630],[573,4107],{"className":4108,"style":774},[773],[573,4110,722],{"className":4111},[778],[573,4113],{"className":4114,"style":774},[773],[573,4116,4118,4121,4124,4127,4130],{"className":4117},[621],[573,4119],{"className":4120,"style":945},[625],[573,4122,927],{"className":4123},[630],[573,4125],{"className":4126,"style":774},[773],[573,4128,2732],{"className":4129},[778],[573,4131],{"className":4132,"style":774},[773],[573,4134,4136,4139,4142,4145,4148],{"className":4135},[621],[573,4137],{"className":4138,"style":964},[625],[573,4140,927],{"className":4141},[630],[573,4143],{"className":4144,"style":774},[773],[573,4146,722],{"className":4147},[778],[573,4149],{"className":4150,"style":774},[773],[573,4152,4154,4157,4160,4163,4166],{"className":4153},[621],[573,4155],{"className":4156,"style":964},[625],[573,4158,607],{"className":4159},[630],[573,4161],{"className":4162,"style":826},[773],[573,4164,735],{"className":4165},[830],[573,4167],{"className":4168,"style":826},[773],[573,4170,4172,4175],{"className":4171},[621],[573,4173],{"className":4174,"style":964},[625],[573,4176,3290],{"className":4177},[630],[573,4179,4181,4207],{"className":4180},[576],[573,4182,4184],{"className":4183},[580],[582,4185,4186],{"xmlns":584},[586,4187,4188,4204],{},[589,4189,4190,4192,4194,4196,4198,4200,4202],{},[605,4191,927],{},[601,4193,2732],{},[605,4195,1824],{},[601,4197,722],{},[605,4199,607],{},[601,4201,735],{},[605,4203,3044],{},[609,4205,4206],{"encoding":611},"2 + 4 \\cdot 1 = 6",[573,4208,4210,4228,4246,4264],{"className":4209,"ariaHidden":617},[616],[573,4211,4213,4216,4219,4222,4225],{"className":4212},[621],[573,4214],{"className":4215,"style":945},[625],[573,4217,927],{"className":4218},[630],[573,4220],{"className":4221,"style":774},[773],[573,4223,2732],{"className":4224},[778],[573,4226],{"className":4227,"style":774},[773],[573,4229,4231,4234,4237,4240,4243],{"className":4230},[621],[573,4232],{"className":4233,"style":964},[625],[573,4235,1824],{"className":4236},[630],[573,4238],{"className":4239,"style":774},[773],[573,4241,722],{"className":4242},[778],[573,4244],{"className":4245,"style":774},[773],[573,4247,4249,4252,4255,4258,4261],{"className":4248},[621],[573,4250],{"className":4251,"style":964},[625],[573,4253,607],{"className":4254},[630],[573,4256],{"className":4257,"style":826},[773],[573,4259,735],{"className":4260},[830],[573,4262],{"className":4263,"style":826},[773],[573,4265,4267,4270],{"className":4266},[621],[573,4268],{"className":4269,"style":964},[625],[573,4271,3044],{"className":4272},[630],[559,4274,4276],{"id":4275},"typische-fehler","Typische Fehler",[4278,4279,4280,4397,4671,4736],"ul",{},[973,4281,4282,4283,1010,4311,4339,4340,1010,4368,4396],{},"Die Nebendiagonale tauschen statt negieren. Richtig: ",[573,4284,4286,4299],{"className":4285},[576],[573,4287,4289],{"className":4288},[580],[582,4290,4291],{"xmlns":584},[586,4292,4293,4297],{},[589,4294,4295],{},[595,4296,994],{},[609,4298,994],{"encoding":611},[573,4300,4302],{"className":4301,"ariaHidden":617},[616],[573,4303,4305,4308],{"className":4304},[621],[573,4306],{"className":4307,"style":1006},[625],[573,4309,994],{"className":4310},[630,634],[573,4312,4314,4327],{"className":4313},[576],[573,4315,4317],{"className":4316},[580],[582,4318,4319],{"xmlns":584},[586,4320,4321,4325],{},[589,4322,4323],{},[595,4324,1025],{},[609,4326,1025],{"encoding":611},[573,4328,4330],{"className":4329,"ariaHidden":617},[616],[573,4331,4333,4336],{"className":4332},[621],[573,4334],{"className":4335,"style":1037},[625],[573,4337,1025],{"className":4338},[630,634]," tauschen die Plätze, ",[573,4341,4343,4356],{"className":4342},[576],[573,4344,4346],{"className":4345},[580],[582,4347,4348],{"xmlns":584},[586,4349,4350,4354],{},[589,4351,4352],{},[595,4353,1062],{},[609,4355,1062],{"encoding":611},[573,4357,4359],{"className":4358,"ariaHidden":617},[616],[573,4360,4362,4365],{"className":4361},[621],[573,4363],{"className":4364,"style":1037},[625],[573,4366,1062],{"className":4367},[630,634],[573,4369,4371,4384],{"className":4370},[576],[573,4372,4374],{"className":4373},[580],[582,4375,4376],{"xmlns":584},[586,4377,4378,4382],{},[589,4379,4380],{},[595,4381,1091],{},[609,4383,1091],{"encoding":611},[573,4385,4387],{"className":4386,"ariaHidden":617},[616],[573,4388,4390,4393],{"className":4389},[621],[573,4391],{"className":4392,"style":1006},[625],[573,4394,1091],{"className":4395},[630,634]," bleiben an ihrem Platz und bekommen nur ein Minus.",[973,4398,4399,4400,1992,4468,4471,4472],{},"Jeden Eintrag einzeln invertieren. ",[573,4401,4403,4424],{"className":4402},[576],[573,4404,4406],{"className":4405},[580],[582,4407,4408],{"xmlns":584},[586,4409,4410,4422],{},[589,4411,4412],{},[592,4413,4414,4416],{},[595,4415,597],{},[589,4417,4418,4420],{},[601,4419,603],{},[605,4421,607],{},[609,4423,612],{"encoding":611},[573,4425,4427],{"className":4426,"ariaHidden":617},[616],[573,4428,4430,4433],{"className":4429},[621],[573,4431],{"className":4432,"style":626},[625],[573,4434,4436,4439],{"className":4435},[630],[573,4437,597],{"className":4438},[630,634],[573,4440,4442],{"className":4441},[638],[573,4443,4445],{"className":4444},[642],[573,4446,4448],{"className":4447},[646],[573,4449,4451],{"className":4450,"style":626},[650],[573,4452,4453,4456],{"style":653},[573,4454],{"className":4455,"style":658},[657],[573,4457,4459],{"className":4458},[662,663,664,665],[573,4460,4462,4465],{"className":4461},[630,665],[573,4463,603],{"className":4464},[630,665],[573,4466,607],{"className":4467},[630,665],[568,4469,4470],{},"nicht"," die Matrix der Kehrwerte ",[573,4473,4475,4506],{"className":4474},[576],[573,4476,4478],{"className":4477},[580],[582,4479,4480],{"xmlns":584},[586,4481,4482,4503],{},[589,4483,4484,4490,4492,4498,4500],{},[2131,4485,4486,4488],{},[605,4487,607],{},[595,4489,994],{},[601,4491,2551],{"separator":617},[2131,4493,4494,4496],{},[605,4495,607],{},[595,4497,1062],{},[601,4499,2551],{"separator":617},[601,4501,4502],{},"…",[609,4504,4505],{"encoding":611},"\\frac{1}{a}, \\frac{1}{b}, \\ldots",[573,4507,4509],{"className":4508,"ariaHidden":617},[616],[573,4510,4512,4516,4588,4591,4594,4662,4665,4668],{"className":4511},[621],[573,4513],{"className":4514,"style":4515},[625],"height:1.1901em;vertical-align:-0.345em;",[573,4517,4519,4522,4585],{"className":4518},[630],[573,4520],{"className":4521},[1866,2301],[573,4523,4525],{"className":4524},[2131],[573,4526,4528,4576],{"className":4527},[642,1886],[573,4529,4531,4573],{"className":4530},[646],[573,4532,4535,4550,4558],{"className":4533,"style":4534},[650],"height:0.8451em;",[573,4536,4538,4541],{"style":4537},"top:-2.655em;",[573,4539],{"className":4540,"style":1473},[657],[573,4542,4544],{"className":4543},[662,663,664,665],[573,4545,4547],{"className":4546},[630,665],[573,4548,994],{"className":4549},[630,634,665],[573,4551,4552,4555],{"style":2329},[573,4553],{"className":4554,"style":1473},[657],[573,4556],{"className":4557,"style":2337},[2336],[573,4559,4561,4564],{"style":4560},"top:-3.394em;",[573,4562],{"className":4563,"style":1473},[657],[573,4565,4567],{"className":4566},[662,663,664,665],[573,4568,4570],{"className":4569},[630,665],[573,4571,607],{"className":4572},[630,665],[573,4574,1922],{"className":4575},[1921],[573,4577,4579],{"className":4578},[646],[573,4580,4583],{"className":4581,"style":4582},[650],"height:0.345em;",[573,4584],{},[573,4586],{"className":4587},[1988,2301],[573,4589,2551],{"className":4590},[2550],[573,4592],{"className":4593,"style":1237},[773],[573,4595,4597,4600,4659],{"className":4596},[630],[573,4598],{"className":4599},[1866,2301],[573,4601,4603],{"className":4602},[2131],[573,4604,4606,4651],{"className":4605},[642,1886],[573,4607,4609,4648],{"className":4608},[646],[573,4610,4612,4626,4634],{"className":4611,"style":4534},[650],[573,4613,4614,4617],{"style":4537},[573,4615],{"className":4616,"style":1473},[657],[573,4618,4620],{"className":4619},[662,663,664,665],[573,4621,4623],{"className":4622},[630,665],[573,4624,1062],{"className":4625},[630,634,665],[573,4627,4628,4631],{"style":2329},[573,4629],{"className":4630,"style":1473},[657],[573,4632],{"className":4633,"style":2337},[2336],[573,4635,4636,4639],{"style":4560},[573,4637],{"className":4638,"style":1473},[657],[573,4640,4642],{"className":4641},[662,663,664,665],[573,4643,4645],{"className":4644},[630,665],[573,4646,607],{"className":4647},[630,665],[573,4649,1922],{"className":4650},[1921],[573,4652,4654],{"className":4653},[646],[573,4655,4657],{"className":4656,"style":4582},[650],[573,4658],{},[573,4660],{"className":4661},[1988,2301],[573,4663,2551],{"className":4664},[2550],[573,4666],{"className":4667,"style":1237},[773],[573,4669,4502],{"className":4670},[1862],[973,4672,4673,4674,4735],{},"Die Formel anwenden, obwohl ",[573,4675,4677,4699],{"className":4676},[576],[573,4678,4680],{"className":4679},[580],[582,4681,4682],{"xmlns":584},[586,4683,4684,4696],{},[589,4685,4686,4688,4690,4692,4694],{},[595,4687,1193],{},[601,4689,1196],{},[595,4691,597],{},[601,4693,735],{},[605,4695,1217],{},[609,4697,4698],{"encoding":611},"\\det A = 0",[573,4700,4702,4726],{"className":4701,"ariaHidden":617},[616],[573,4703,4705,4708,4711,4714,4717,4720,4723],{"className":4704},[621],[573,4706],{"className":4707,"style":1037},[625],[573,4709,1193],{"className":4710},[1233],[573,4712],{"className":4713,"style":1237},[773],[573,4715,597],{"className":4716},[630,634],[573,4718],{"className":4719,"style":826},[773],[573,4721,735],{"className":4722},[830],[573,4724],{"className":4725,"style":826},[773],[573,4727,4729,4732],{"className":4728},[621],[573,4730],{"className":4731,"style":964},[625],[573,4733,1217],{"className":4734},[630]," ist. Dann gibt es keine Inverse.",[973,4737,4738,4923,4924,5034],{},[573,4739,4741,4779],{"className":4740},[576],[573,4742,4744],{"className":4743},[580],[582,4745,4746],{"xmlns":584},[586,4747,4748,4776],{},[589,4749,4750,4756,4758,4764,4766],{},[1422,4751,4752,4754],{"accent":617},[595,4753,1426],{},[601,4755,1429],{},[601,4757,735],{},[1422,4759,4760,4762],{"accent":617},[595,4761,1062],{},[601,4763,1429],{},[601,4765,722],{},[592,4767,4768,4770],{},[595,4769,597],{},[589,4771,4772,4774],{},[601,4773,603],{},[605,4775,607],{},[609,4777,4778],{"encoding":611},"\\vec{x} = \\vec{b} \\cdot A^{-1}",[573,4780,4782,4832,4882],{"className":4781,"ariaHidden":617},[616],[573,4783,4785,4788,4823,4826,4829],{"className":4784},[621],[573,4786],{"className":4787,"style":1450},[625],[573,4789,4791],{"className":4790},[630,1457],[573,4792,4794],{"className":4793},[642],[573,4795,4797],{"className":4796},[646],[573,4798,4800,4808],{"className":4799,"style":1450},[650],[573,4801,4802,4805],{"style":1469},[573,4803],{"className":4804,"style":1473},[657],[573,4806,1426],{"className":4807},[630,634],[573,4809,4810,4813],{"style":1469},[573,4811],{"className":4812,"style":1473},[657],[573,4814,4816],{"className":4815,"style":1486},[1485],[573,4817,4819],{"className":4818,"style":1491},[1490],[1493,4820,4821],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,4822],{"d":1504},[573,4824],{"className":4825,"style":826},[773],[573,4827,735],{"className":4828},[830],[573,4830],{"className":4831,"style":826},[773],[573,4833,4835,4838,4873,4876,4879],{"className":4834},[621],[573,4836],{"className":4837,"style":1520},[625],[573,4839,4841],{"className":4840},[630,1457],[573,4842,4844],{"className":4843},[642],[573,4845,4847],{"className":4846},[646],[573,4848,4850,4858],{"className":4849,"style":1520},[650],[573,4851,4852,4855],{"style":1469},[573,4853],{"className":4854,"style":1473},[657],[573,4856,1062],{"className":4857},[630,634],[573,4859,4860,4863],{"style":1543},[573,4861],{"className":4862,"style":1473},[657],[573,4864,4866],{"className":4865,"style":1550},[1485],[573,4867,4869],{"className":4868,"style":1491},[1490],[1493,4870,4871],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,4872],{"d":1504},[573,4874],{"className":4875,"style":774},[773],[573,4877,722],{"className":4878},[778],[573,4880],{"className":4881,"style":774},[773],[573,4883,4885,4888],{"className":4884},[621],[573,4886],{"className":4887,"style":626},[625],[573,4889,4891,4894],{"className":4890},[630],[573,4892,597],{"className":4893},[630,634],[573,4895,4897],{"className":4896},[638],[573,4898,4900],{"className":4899},[642],[573,4901,4903],{"className":4902},[646],[573,4904,4906],{"className":4905,"style":626},[650],[573,4907,4908,4911],{"style":653},[573,4909],{"className":4910,"style":658},[657],[573,4912,4914],{"className":4913},[662,663,664,665],[573,4915,4917,4920],{"className":4916},[630,665],[573,4918,603],{"className":4919},[630,665],[573,4921,607],{"className":4922},[630,665]," statt ",[573,4925,4927,4955],{"className":4926},[576],[573,4928,4930],{"className":4929},[580],[582,4931,4932],{"xmlns":584},[586,4933,4934,4952],{},[589,4935,4936,4946],{},[592,4937,4938,4940],{},[595,4939,597],{},[589,4941,4942,4944],{},[601,4943,603],{},[605,4945,607],{},[1422,4947,4948,4950],{"accent":617},[595,4949,1062],{},[601,4951,1429],{},[609,4953,4954],{"encoding":611},"A^{-1}\\vec{b}",[573,4956,4958],{"className":4957,"ariaHidden":617},[616],[573,4959,4961,4964,4999],{"className":4960},[621],[573,4962],{"className":4963,"style":1520},[625],[573,4965,4967,4970],{"className":4966},[630],[573,4968,597],{"className":4969},[630,634],[573,4971,4973],{"className":4972},[638],[573,4974,4976],{"className":4975},[642],[573,4977,4979],{"className":4978},[646],[573,4980,4982],{"className":4981,"style":626},[650],[573,4983,4984,4987],{"style":653},[573,4985],{"className":4986,"style":658},[657],[573,4988,4990],{"className":4989},[662,663,664,665],[573,4991,4993,4996],{"className":4992},[630,665],[573,4994,603],{"className":4995},[630,665],[573,4997,607],{"className":4998},[630,665],[573,5000,5002],{"className":5001},[630,1457],[573,5003,5005],{"className":5004},[642],[573,5006,5008],{"className":5007},[646],[573,5009,5011,5019],{"className":5010,"style":1520},[650],[573,5012,5013,5016],{"style":1469},[573,5014],{"className":5015,"style":1473},[657],[573,5017,1062],{"className":5018},[630,634],[573,5020,5021,5024],{"style":1543},[573,5022],{"className":5023,"style":1473},[657],[573,5025,5027],{"className":5026,"style":1550},[1485],[573,5028,5030],{"className":5029,"style":1491},[1490],[1493,5031,5032],{"xmlns":1495,"width":1496,"height":1497,"style":1498,"viewBox":1499,"preserveAspectRatio":1500},[1502,5033],{"d":1504}," rechnen. Die Reihenfolge der Faktoren ist wichtig.",{"title":5036,"searchDepth":5037,"depth":5037,"links":5038},"",2,[5039,5040,5041],{"id":561,"depth":5037,"text":562},{"id":1759,"depth":5037,"text":1760},{"id":4275,"depth":5037,"text":4276},[5043,5045,5047,5049,5051,5054,5056,5058,5060,5062,5064,5066,5068,5070],{"lhs":5044,"rhs":607},"a*d\u002F(a*d - b*c) + b*(-c)\u002F(a*d - b*c)",{"lhs":5046,"rhs":1217},"a*(-b)\u002F(a*d - b*c) + b*a\u002F(a*d - b*c)",{"lhs":5048,"rhs":1217},"c*d\u002F(a*d - b*c) + d*(-c)\u002F(a*d - b*c)",{"lhs":5050,"rhs":607},"c*(-b)\u002F(a*d - b*c) + d*a\u002F(a*d - b*c)",{"lhs":5052,"rhs":5053},"inv([[a, b], [c, d]])[1, 2]","-b\u002F(a*d - b*c)",{"lhs":5055,"rhs":2024},"3*4 - 2*1",{"lhs":5057,"rhs":607},"3*0.4 + 2*(-0.1)",{"lhs":5059,"rhs":1217},"3*(-0.2) + 2*0.3",{"lhs":5061,"rhs":1217},"1*0.4 + 4*(-0.1)",{"lhs":5063,"rhs":607},"1*(-0.2) + 4*0.3",{"lhs":5065,"rhs":927},"0.4*8 + (-0.2)*6",{"lhs":5067,"rhs":607},"(-0.1)*8 + 0.3*6",{"lhs":5069,"rhs":3290},"3*2 + 2*1",{"lhs":5071,"rhs":3044},"2 + 4*1","A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix},\\ ad - bc \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">ad - bc \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","inverse-2x2","A^{-1} = \\frac{1}{ad - bc} \\begin{pmatrix} d & -b \\\\ -c & a \\end{pmatrix}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{-1} = \\frac{1}{ad - bc} \\begin{pmatrix} d & -b \\\\ -c & a \\end{pmatrix}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7693em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-2x2-matrix",[],[5085,5086,5087],"determinant-2x2","matrix-multiplication","cramers-rule",{"title":548,"description":5036},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-2x2-matrix","Die Inverse einer 2×2-Matrix erhält man durch Tauschen der Diagonale, Negieren der Nebendiagonale und Teilen durch die Determinante.",[5092,5093,5094,5095],"matrix","inverse","determinante","gleichungssystem",[5097,5100,5104,5107],{"symbol":597,"meaning":5098,"symbolHtml":5099},"invertierbare 2×2-Matrix mit den Einträgen a, b, c, d","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5101,"meaning":5102,"symbolHtml":5103},"a, b, c, d","Einträge von A (a, b in der ersten Zeile, c, d in der zweiten)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c, d\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1137,"meaning":5105,"symbolHtml":5106},"Determinante von A","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">ad - bc\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":612,"meaning":5108,"symbolHtml":5109},"inverse Matrix, es gilt A · A⁻¹ = A⁻¹ · A = E (Einheitsmatrix)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{-1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","-eqW_qmF5DlwaNm4AJDxAjBoXRZfbAuDpLdqyagEb-0",[5112,5115,5118],{"stem":5113,"title":5114,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fcramersche-regel","Cramersche Regel",{"stem":5116,"title":5117,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdeterminante-2x2","Determinante einer 2×2-Matrix",{"stem":5119,"title":5120,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmatrizenmultiplikation","Matrizenmultiplikation",1793824278273]