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Strichen.",[559,1045,1047],{"id":1046},"beispiele","Beispiele",[573,1049,1052],{"className":1050},[1051],"katex-display",[573,1053,1055,1144],{"className":1054},[576],[573,1056,1058],{"className":1057},[580],[582,1059,1061],{"xmlns":584,"display":1060},"block",[586,1062,1063,1141],{},[589,1064,1065,1067,1069,1118,1120,1122,1125,1127,1130,1132,1134,1136,1138],{},[677,1066,679],{},[596,1068,682],{},[589,1070,1071,1074,1115],{},[596,1072,1073],{"fence":610},"(",[1075,1076,1080,1099],"mtable",{"rowspacing":1077,"columnalign":1078,"columnspacing":1079},"0.16em","center 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10",[573,1145,1147,1308,1326,1344,1362,1380],{"className":1146,"ariaHidden":610},[609],[573,1148,1150,1154,1157,1160,1299,1302,1305],{"className":1149},[614],[573,1151],{"className":1152,"style":1153},[618],"height:2.4em;vertical-align:-0.95em;",[573,1155,679],{"className":1156},[709],[573,1158],{"className":1159,"style":713},[627],[573,1161,1164,1175,1292],{"className":1162},[1163],"minner",[573,1165,1170],{"className":1166,"style":1169},[1167,1168],"mopen","delimcenter","top:0em;",[573,1171,1073],{"className":1172},[1173,1174],"delimsizing","size3",[573,1176,1178],{"className":1177},[623],[573,1179,1181,1239,1244,1247],{"className":1180},[1075],[573,1182,1185],{"className":1183},[1184],"col-align-c",[573,1186,1190,1230],{"className":1187},[1188,1189],"vlist-t","vlist-t2",[573,1191,1194,1225],{"className":1192},[1193],"vlist-r",[573,1195,1199,1213],{"className":1196,"style":1198},[1197],"vlist","height:1.45em;",[573,1200,1202,1207],{"style":1201},"top:-3.61em;",[573,1203],{"className":1204,"style":1206},[1205],"pstrut","height:3em;",[573,1208,1210],{"className":1209},[623],[573,1211,1092],{"className":1212},[623],[573,1214,1216,1219],{"style":1215},"top:-2.41em;",[573,1217],{"className":1218,"style":1206},[1205],[573,1220,1222],{"className":1221},[623],[573,1223,1107],{"className":1224},[623],[573,1226,1229],{"className":1227},[1228],"vlist-s","​",[573,1231,1233],{"className":1232},[1193],[573,1234,1237],{"className":1235,"style":1236},[1197],"height:0.95em;",[573,1238],{},[573,1240],{"className":1241,"style":1243},[1242],"arraycolsep","width:0.5em;",[573,1245],{"className":1246,"style":1243},[1242],[573,1248,1250],{"className":1249},[1184],[573,1251,1253,1284],{"className":1252},[1188,1189],[573,1254,1256,1281],{"className":1255},[1193],[573,1257,1259,1270],{"className":1258,"style":1198},[1197],[573,1260,1261,1264],{"style":1201},[573,1262],{"className":1263,"style":1206},[1205],[573,1265,1267],{"className":1266},[623],[573,1268,594],{"className":1269},[623],[573,1271,1272,1275],{"style":1215},[573,1273],{"className":1274,"style":1206},[1205],[573,1276,1278],{"className":1277},[623],[573,1279,1114],{"className":1280},[623],[573,1282,1229],{"className":1283},[1228],[573,1285,1287],{"className":1286},[1193],[573,1288,1290],{"className":1289,"style":1236},[1197],[573,1291],{},[573,1293,1296],{"className":1294,"style":1169},[1295,1168],"mclose",[573,1297,1117],{"className":1298},[1173,1174],[573,1300],{"className":1301,"style":721},[627],[573,1303,766],{"className":1304},[725],[573,1306],{"className":1307,"style":721},[627],[573,1309,1311,1314,1317,1320,1323],{"className":1310},[614],[573,1312],{"className":1313,"style":642},[618],[573,1315,1092],{"className":1316},[623],[573,1318],{"className":1319,"style":628},[627],[573,1321,1124],{"className":1322},[632],[573,1324],{"className":1325,"style":628},[627],[573,1327,1329,1332,1335,1338,1341],{"className":1328},[614],[573,1330],{"className":1331,"style":619},[618],[573,1333,1114],{"className":1334},[623],[573,1336],{"className":1337,"style":628},[627],[573,1339,1129],{"className":1340},[632],[573,1342],{"className":1343,"style":628},[627],[573,1345,1347,1350,1353,1356,1359],{"className":1346},[614],[573,1348],{"className":1349,"style":642},[618],[573,1351,594],{"className":1352},[623],[573,1354],{"className":1355,"style":628},[627],[573,1357,1124],{"className":1358},[632],[573,1360],{"className":1361,"style":628},[627],[573,1363,1365,1368,1371,1374,1377],{"className":1364},[614],[573,1366],{"className":1367,"style":642},[618],[573,1369,1107],{"className":1370},[623],[573,1372],{"className":1373,"style":721},[627],[573,1375,766],{"className":1376},[725],[573,1378],{"className":1379,"style":721},[627],[573,1381,1383,1386],{"className":1382},[614],[573,1384],{"className":1385,"style":642},[618],[573,1387,1140],{"className":1388},[623],[573,1390,1392],{"className":1391},[1051],[573,1393,1395,1468],{"className":1394},[576],[573,1396,1398],{"className":1397},[580],[582,1399,1400],{"xmlns":584,"display":1060},[586,1401,1402,1465],{},[589,1403,1404,1406,1408,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463],{},[677,1405,679],{},[596,1407,682],{},[589,1409,1410,1412,1443],{},[596,1411,1073],{"fence":610},[1075,1413,1414,1429],{"rowspacing":1077,"columnalign":1078,"columnspacing":1079},[1081,1415,1416,1422],{},[1084,1417,1418],{},[1087,1419,1420],{"scriptlevel":692,"displaystyle":1089},[592,1421,594],{},[1084,1423,1424],{},[1087,1425,1426],{"scriptlevel":692,"displaystyle":1089},[592,1427,1428],{},"6",[1081,1430,1431,1437],{},[1084,1432,1433],{},[1087,1434,1435],{"scriptlevel":692,"displaystyle":1089},[592,1436,1107],{},[1084,1438,1439],{},[1087,1440,1441],{"scriptlevel":692,"displaystyle":1089},[592,1442,1092],{},[596,1444,1117],{"fence":610},[596,1446,766],{},[592,1448,594],{},[596,1450,1124],{},[592,1452,1092],{},[596,1454,1129],{},[592,1456,1428],{},[596,1458,1124],{},[592,1460,1107],{},[596,1462,766],{},[592,1464,692],{},[602,1466,1467],{"encoding":604},"\\det \\begin{pmatrix} 2 & 6 \\\\ 1 & 3 \\end{pmatrix} = 2 \\cdot 3 - 6 \\cdot 1 = 0",[573,1469,1471,1609,1627,1645,1663,1681],{"className":1470,"ariaHidden":610},[609],[573,1472,1474,1477,1480,1483,1600,1603,1606],{"className":1473},[614],[573,1475],{"className":1476,"style":1153},[618],[573,1478,679],{"className":1479},[709],[573,1481],{"className":1482,"style":713},[627],[573,1484,1486,1492,1594],{"className":1485},[1163],[573,1487,1489],{"className":1488,"style":1169},[1167,1168],[573,1490,1073],{"className":1491},[1173,1174],[573,1493,1495],{"className":1494},[623],[573,1496,1498,1543,1546,1549],{"className":1497},[1075],[573,1499,1501],{"className":1500},[1184],[573,1502,1504,1535],{"className":1503},[1188,1189],[573,1505,1507,1532],{"className":1506},[1193],[573,1508,1510,1521],{"className":1509,"style":1198},[1197],[573,1511,1512,1515],{"style":1201},[573,1513],{"className":1514,"style":1206},[1205],[573,1516,1518],{"className":1517},[623],[573,1519,594],{"className":1520},[623],[573,1522,1523,1526],{"style":1215},[573,1524],{"className":1525,"style":1206},[1205],[573,1527,1529],{"className":1528},[623],[573,1530,1107],{"className":1531},[623],[573,1533,1229],{"className":1534},[1228],[573,1536,1538],{"className":1537},[1193],[573,1539,1541],{"className":1540,"style":1236},[1197],[573,1542],{},[573,1544],{"className":1545,"style":1243},[1242],[573,1547],{"className":1548,"style":1243},[1242],[573,1550,1552],{"className":1551},[1184],[573,1553,1555,1586],{"className":1554},[1188,1189],[573,1556,1558,1583],{"className":1557},[1193],[573,1559,1561,1572],{"className":1560,"style":1198},[1197],[573,1562,1563,1566],{"style":1201},[573,1564],{"className":1565,"style":1206},[1205],[573,1567,1569],{"className":1568},[623],[573,1570,1428],{"className":1571},[623],[573,1573,1574,1577],{"style":1215},[573,1575],{"className":1576,"style":1206},[1205],[573,1578,1580],{"className":1579},[623],[573,1581,1092],{"className":1582},[623],[573,1584,1229],{"className":1585},[1228],[573,1587,1589],{"className":1588},[1193],[573,1590,1592],{"className":1591,"style":1236},[1197],[573,1593],{},[573,1595,1597],{"className":1596,"style":1169},[1295,1168],[573,1598,1117],{"className":1599},[1173,1174],[573,1601],{"className":1602,"style":721},[627],[573,1604,766],{"className":1605},[725],[573,1607],{"className":1608,"style":721},[627],[573,1610,1612,1615,1618,1621,1624],{"className":1611},[614],[573,1613],{"className":1614,"style":642},[618],[573,1616,594],{"className":1617},[623],[573,1619],{"className":1620,"style":628},[627],[573,1622,1124],{"className":1623},[632],[573,1625],{"className":1626,"style":628},[627],[573,1628,1630,1633,1636,1639,1642],{"className":1629},[614],[573,1631],{"className":1632,"style":619},[618],[573,1634,1092],{"className":1635},[623],[573,1637],{"className":1638,"style":628},[627],[573,1640,1129],{"className":1641},[632],[573,1643],{"className":1644,"style":628},[627],[573,1646,1648,1651,1654,1657,1660],{"className":1647},[614],[573,1649],{"className":1650,"style":642},[618],[573,1652,1428],{"className":1653},[623],[573,1655],{"className":1656,"style":628},[627],[573,1658,1124],{"className":1659},[632],[573,1661],{"className":1662,"style":628},[627],[573,1664,1666,1669,1672,1675,1678],{"className":1665},[614],[573,1667],{"className":1668,"style":642},[618],[573,1670,1107],{"className":1671},[623],[573,1673],{"className":1674,"style":721},[627],[573,1676,766],{"className":1677},[725],[573,1679],{"className":1680,"style":721},[627],[573,1682,1684,1687],{"className":1683},[614],[573,1685],{"className":1686,"style":642},[618],[573,1688,692],{"className":1689},[623],[564,1691,1692],{},"Die erste Zeile ist das Doppelte der zweiten. Ein Gleichungssystem mit dieser Koeffizientenmatrix ist nicht eindeutig lösbar.",[564,1694,1695],{},"Mit negativen Einträgen:",[573,1697,1699],{"className":1698},[1051],[573,1700,1702,1806],{"className":1701},[576],[573,1703,1705],{"className":1704},[580],[582,1706,1707],{"xmlns":584,"display":1060},[586,1708,1709,1803],{},[589,1710,1711,1713,1715,1760,1762,1764,1766,1768,1770,1772,1774,1776,1778,1780,1782,1784,1786,1788,1790,1792,1794,1797,1799,1801],{},[677,1712,679],{},[596,1714,682],{},[589,1716,1717,1719,1758],{},[596,1718,1073],{"fence":610},[1075,1720,1721,1739],{"rowspacing":1077,"columnalign":1078,"columnspacing":1079},[1081,1722,1723,1733],{},[1084,1724,1725],{},[1087,1726,1727],{"scriptlevel":692,"displaystyle":1089},[589,1728,1729,1731],{},[596,1730,1129],{},[592,1732,1107],{},[1084,1734,1735],{},[1087,1736,1737],{"scriptlevel":692,"displaystyle":1089},[592,1738,1092],{},[1081,1740,1741,1751],{},[1084,1742,1743],{},[1087,1744,1745],{"scriptlevel":692,"displaystyle":1089},[589,1746,1747,1749],{},[596,1748,1129],{},[592,1750,594],{},[1084,1752,1753],{},[1087,1754,1755],{"scriptlevel":692,"displaystyle":1089},[592,1756,1757],{},"5",[596,1759,1117],{"fence":610},[596,1761,766],{},[596,1763,1073],{"stretchy":1089},[596,1765,1129],{},[592,1767,1107],{},[596,1769,1117],{"stretchy":1089},[596,1771,1124],{},[592,1773,1757],{},[596,1775,1129],{},[592,1777,1092],{},[596,1779,1124],{},[596,1781,1073],{"stretchy":1089},[596,1783,1129],{},[592,1785,594],{},[596,1787,1117],{"stretchy":1089},[596,1789,766],{},[596,1791,1129],{},[592,1793,1757],{},[596,1795,1796],{},"+",[592,1798,1428],{},[596,1800,766],{},[592,1802,1107],{},[602,1804,1805],{"encoding":604},"\\det \\begin{pmatrix} -1 & 3 \\\\ -2 & 5 \\end{pmatrix} = (-1) \\cdot 5 - 3 \\cdot (-2) = -5 + 6 = 1",[573,1807,1809,1953,1980,1998,2016,2043,2064,2082],{"className":1808,"ariaHidden":610},[609],[573,1810,1812,1815,1818,1821,1944,1947,1950],{"className":1811},[614],[573,1813],{"className":1814,"style":1153},[618],[573,1816,679],{"className":1817},[709],[573,1819],{"className":1820,"style":713},[627],[573,1822,1824,1830,1938],{"className":1823},[1163],[573,1825,1827],{"className":1826,"style":1169},[1167,1168],[573,1828,1073],{"className":1829},[1173,1174],[573,1831,1833],{"className":1832},[623],[573,1834,1836,1887,1890,1893],{"className":1835},[1075],[573,1837,1839],{"className":1838},[1184],[573,1840,1842,1879],{"className":1841},[1188,1189],[573,1843,1845,1876],{"className":1844},[1193],[573,1846,1848,1862],{"className":1847,"style":1198},[1197],[573,1849,1850,1853],{"style":1201},[573,1851],{"className":1852,"style":1206},[1205],[573,1854,1856,1859],{"className":1855},[623],[573,1857,1129],{"className":1858},[623],[573,1860,1107],{"className":1861},[623],[573,1863,1864,1867],{"style":1215},[573,1865],{"className":1866,"style":1206},[1205],[573,1868,1870,1873],{"className":1869},[623],[573,1871,1129],{"className":1872},[623],[573,1874,594],{"className":1875},[623],[573,1877,1229],{"className":1878},[1228],[573,1880,1882],{"className":1881},[1193],[573,1883,1885],{"className":1884,"style":1236},[1197],[573,1886],{},[573,1888],{"className":1889,"style":1243},[1242],[573,1891],{"className":1892,"style":1243},[1242],[573,1894,1896],{"className":1895},[1184],[573,1897,1899,1930],{"className":1898},[1188,1189],[573,1900,1902,1927],{"className":1901},[1193],[573,1903,1905,1916],{"className":1904,"style":1198},[1197],[573,1906,1907,1910],{"style":1201},[573,1908],{"className":1909,"style":1206},[1205],[573,1911,1913],{"className":1912},[623],[573,1914,1092],{"className":1915},[623],[573,1917,1918,1921],{"style":1215},[573,1919],{"className":1920,"style":1206},[1205],[573,1922,1924],{"className":1923},[623],[573,1925,1757],{"className":1926},[623],[573,1928,1229],{"className":1929},[1228],[573,1931,1933],{"className":1932},[1193],[573,1934,1936],{"className":1935,"style":1236},[1197],[573,1937],{},[573,1939,1941],{"className":1940,"style":1169},[1295,1168],[573,1942,1117],{"className":1943},[1173,1174],[573,1945],{"className":1946,"style":721},[627],[573,1948,766],{"className":1949},[725],[573,1951],{"className":1952,"style":721},[627],[573,1954,1956,1959,1962,1965,1968,1971,1974,1977],{"className":1955},[614],[573,1957],{"className":1958,"style":941},[618],[573,1960,1073],{"className":1961},[1167],[573,1963,1129],{"className":1964},[623],[573,1966,1107],{"className":1967},[623],[573,1969,1117],{"className":1970},[1295],[573,1972],{"className":1973,"style":628},[627],[573,1975,1124],{"className":1976},[632],[573,1978],{"className":1979,"style":628},[627],[573,1981,1983,1986,1989,1992,1995],{"className":1982},[614],[573,1984],{"className":1985,"style":619},[618],[573,1987,1757],{"className":1988},[623],[573,1990],{"className":1991,"style":628},[627],[573,1993,1129],{"className":1994},[632],[573,1996],{"className":1997,"style":628},[627],[573,1999,2001,2004,2007,2010,2013],{"className":2000},[614],[573,2002],{"className":2003,"style":642},[618],[573,2005,1092],{"className":2006},[623],[573,2008],{"className":2009,"style":628},[627],[573,2011,1124],{"className":2012},[632],[573,2014],{"className":2015,"style":628},[627],[573,2017,2019,2022,2025,2028,2031,2034,2037,2040],{"className":2018},[614],[573,2020],{"className":2021,"style":941},[618],[573,2023,1073],{"className":2024},[1167],[573,2026,1129],{"className":2027},[623],[573,2029,594],{"className":2030},[623],[573,2032,1117],{"className":2033},[1295],[573,2035],{"className":2036,"style":721},[627],[573,2038,766],{"className":2039},[725],[573,2041],{"className":2042,"style":721},[627],[573,2044,2046,2049,2052,2055,2058,2061],{"className":2045},[614],[573,2047],{"className":2048,"style":619},[618],[573,2050,1129],{"className":2051},[623],[573,2053,1757],{"className":2054},[623],[573,2056],{"className":2057,"style":628},[627],[573,2059,1796],{"className":2060},[632],[573,2062],{"className":2063,"style":628},[627],[573,2065,2067,2070,2073,2076,2079],{"className":2066},[614],[573,2068],{"className":2069,"style":642},[618],[573,2071,1428],{"className":2072},[623],[573,2074],{"className":2075,"style":721},[627],[573,2077,766],{"className":2078},[725],[573,2080],{"className":2081,"style":721},[627],[573,2083,2085,2088],{"className":2084},[614],[573,2086],{"className":2087,"style":642},[618],[573,2089,1107],{"className":2090},[623],[559,2092,2094],{"id":2093},"typische-fehler","Typische Fehler",[659,2096,2097,2248,2318],{},[662,2098,2099,2100,2218,2219,2247],{},"Die Produkte addieren statt subtrahieren: ",[573,2101,2103,2134],{"className":2102},[576],[573,2104,2106],{"className":2105},[580],[582,2107,2108],{"xmlns":584},[586,2109,2110,2131],{},[589,2111,2112,2114,2116,2118,2120,2122,2124,2126,2128],{},[592,2113,1092],{},[596,2115,1124],{},[592,2117,1114],{},[596,2119,1796],{},[592,2121,594],{},[596,2123,1124],{},[592,2125,1107],{},[596,2127,766],{},[592,2129,2130],{},"14",[602,2132,2133],{"encoding":604},"3 \\cdot 4 + 2 \\cdot 1 = 14",[573,2135,2137,2155,2173,2191,2209],{"className":2136,"ariaHidden":610},[609],[573,2138,2140,2143,2146,2149,2152],{"className":2139},[614],[573,2141],{"className":2142,"style":642},[618],[573,2144,1092],{"className":2145},[623],[573,2147],{"className":2148,"style":628},[627],[573,2150,1124],{"className":2151},[632],[573,2153],{"className":2154,"style":628},[627],[573,2156,2158,2161,2164,2167,2170],{"className":2157},[614],[573,2159],{"className":2160,"style":619},[618],[573,2162,1114],{"className":2163},[623],[573,2165],{"className":2166,"style":628},[627],[573,2168,1796],{"className":2169},[632],[573,2171],{"className":2172,"style":628},[627],[573,2174,2176,2179,2182,2185,2188],{"className":2175},[614],[573,2177],{"className":2178,"style":642},[618],[573,2180,594],{"className":2181},[623],[573,2183],{"className":2184,"style":628},[627],[573,2186,1124],{"className":2187},[632],[573,2189],{"className":2190,"style":628},[627],[573,2192,2194,2197,2200,2203,2206],{"className":2193},[614],[573,2195],{"className":2196,"style":642},[618],[573,2198,1107],{"className":2199},[623],[573,2201],{"className":2202,"style":721},[627],[573,2204,766],{"className":2205},[725],[573,2207],{"className":2208,"style":721},[627],[573,2210,2212,2215],{"className":2211},[614],[573,2213],{"className":2214,"style":642},[618],[573,2216,2130],{"className":2217},[623]," ist falsch, richtig ist ",[573,2220,2222,2235],{"className":2221},[576],[573,2223,2225],{"className":2224},[580],[582,2226,2227],{"xmlns":584},[586,2228,2229,2233],{},[589,2230,2231],{},[592,2232,1140],{},[602,2234,1140],{"encoding":604},[573,2236,2238],{"className":2237,"ariaHidden":610},[609],[573,2239,2241,2244],{"className":2240},[614],[573,2242],{"className":2243,"style":642},[618],[573,2245,1140],{"className":2246},[623],".",[662,2249,2250,2251,2317],{},"Die Reihenfolge vertauschen und ",[573,2252,2254,2280],{"className":2253},[576],[573,2255,2257],{"className":2256},[580],[582,2258,2259],{"xmlns":584},[586,2260,2261,2277],{},[589,2262,2263,2266,2269,2271,2274],{},[677,2264,2265],{},"b",[677,2267,2268],{},"c",[596,2270,1129],{},[677,2272,2273],{},"a",[677,2275,2276],{},"d",[602,2278,2279],{"encoding":604},"bc - ad",[573,2281,2283,2305],{"className":2282,"ariaHidden":610},[609],[573,2284,2286,2290,2293,2296,2299,2302],{"className":2285},[614],[573,2287],{"className":2288,"style":2289},[618],"height:0.7778em;vertical-align:-0.0833em;",[573,2291,2265],{"className":2292},[623,717],[573,2294,2268],{"className":2295},[623,717],[573,2297],{"className":2298,"style":628},[627],[573,2300,1129],{"className":2301},[632],[573,2303],{"className":2304,"style":628},[627],[573,2306,2308,2311,2314],{"className":2307},[614],[573,2309],{"className":2310,"style":875},[618],[573,2312,2273],{"className":2313},[623,717],[573,2315,2276],{"className":2316},[623,717]," rechnen. Das ergibt das falsche Vorzeichen.",[662,2319,2320,2321,2247],{},"Vorzeichenfehler bei negativen Einträgen: ",[573,2322,2324,2356],{"className":2323},[576],[573,2325,2327],{"className":2326},[580],[582,2328,2329],{"xmlns":584},[586,2330,2331,2353],{},[589,2332,2333,2335,2337,2339,2341,2343,2345,2347,2349,2351],{},[596,2334,1129],{},[592,2336,1092],{},[596,2338,1124],{},[596,2340,1073],{"stretchy":1089},[596,2342,1129],{},[592,2344,594],{},[596,2346,1117],{"stretchy":1089},[596,2348,766],{},[596,2350,1796],{},[592,2352,1428],{},[602,2354,2355],{"encoding":604},"-3 \\cdot (-2) = +6",[573,2357,2359,2380,2407],{"className":2358,"ariaHidden":610},[609],[573,2360,2362,2365,2368,2371,2374,2377],{"className":2361},[614],[573,2363],{"className":2364,"style":619},[618],[573,2366,1129],{"className":2367},[623],[573,2369,1092],{"className":2370},[623],[573,2372],{"className":2373,"style":628},[627],[573,2375,1124],{"className":2376},[632],[573,2378],{"className":2379,"style":628},[627],[573,2381,2383,2386,2389,2392,2395,2398,2401,2404],{"className":2382},[614],[573,2384],{"className":2385,"style":941},[618],[573,2387,1073],{"className":2388},[1167],[573,2390,1129],{"className":2391},[623],[573,2393,594],{"className":2394},[623],[573,2396,1117],{"className":2397},[1295],[573,2399],{"className":2400,"style":721},[627],[573,2402,766],{"className":2403},[725],[573,2405],{"className":2406,"style":721},[627],[573,2408,2410,2413,2416],{"className":2409},[614],[573,2411],{"className":2412,"style":619},[618],[573,2414,1796],{"className":2415},[623],[573,2417,1428],{"className":2418},[623],{"title":2420,"searchDepth":2421,"depth":2421,"links":2422},"",2,[2423,2424,2425],{"id":561,"depth":2421,"text":562},{"id":1046,"depth":2421,"text":1047},{"id":2093,"depth":2421,"text":2094},[2427,2430,2433,2435,2437,2439,2441],{"lhs":2428,"rhs":2429},"det([[a, b], [c, d]])","a*d - b*c",{"lhs":2431,"rhs":2432},"c*b - d*a","-(a*d - b*c)",{"lhs":2434,"rhs":1140},"3*4 - 2*1",{"lhs":2436,"rhs":1140},"det([[3, 2], [1, 4]])",{"lhs":2438,"rhs":692},"2*3 - 6*1",{"lhs":2440,"rhs":1107},"(-1)*5 - 3*(-2)",{"lhs":2442,"rhs":2130},"3*4 + 2*1",null,"md","determinant-2x2","\\det \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} = ad - bc","\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>\u003Cmi>det\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>=\u003C\u002Fmo>\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\">\\det \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} = 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:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\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\">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:0.2778em;\">\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: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>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdeterminante-2x2",[],[2454,2455,2456,2457],"determinant-3x3","inverse-2x2","cramers-rule","parallelogram-area-vectors",{"title":548,"description":2420},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdeterminante-2x2","Die Determinante einer 2×2-Matrix ist das Produkt der Hauptdiagonale minus das Produkt der Nebendiagonale.",[2462,2463,2464,2465],"determinante","matrix","gleichungssystem","flächeninhalt",[2467,2471],{"symbol":2468,"meaning":2469,"symbolHtml":2470},"a, d","Einträge auf der Hauptdiagonalen (oben links, unten rechts)","\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>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, 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\" 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class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","R7FFmF01A0SXdmj-egyjmU2IR8vVkEkNlmm3mXbQ5Yg",[2477,2480,2483,2486],{"stem":2478,"title":2479,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fcramersche-regel","Cramersche Regel",{"stem":2481,"title":2482,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdeterminante-3x3","Determinante einer 3×3-Matrix (Regel von Sarrus)",{"stem":2484,"title":2485,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fflaecheninhalt-parallelogramm-vektoren","Flächeninhalt eines Parallelogramms mit Vektoren",{"stem":2487,"title":2488,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-2x2-matrix","Inverse einer 2×2-Matrix",1793824277644]