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r",[573,1096,1098,1125,1179],{"className":1097,"ariaHidden":598},[624],[573,1099,1101,1104,1110,1113,1116,1119,1122],{"className":1100},[628],[573,1102],{"className":1103,"style":980},[632],[573,1105,1107],{"className":1106},[984],[573,1108,935],{"className":1109,"style":989},[637,988],[573,1111,942],{"className":1112},[993],[573,1114,594],{"className":1115},[637,638],[573,1117],{"className":1118,"style":698},[697],[573,1120,1078],{"className":1121},[702],[573,1123],{"className":1124,"style":698},[697],[573,1126,1128,1132,1167,1170,1173,1176],{"className":1127},[628],[573,1129],{"className":1130,"style":1131},[632],"height:1.2274em;vertical-align:-0.25em;",[573,1133,1135],{"className":1134},[637,642],[573,1136,1138],{"className":1137},[646],[573,1139,1141],{"className":1140},[650],[573,1142,1144,1152],{"className":1143,"style":712},[654],[573,1145,1146,1149],{"style":657},[573,1147],{"className":1148,"style":662},[661],[573,1150,613],{"className":1151},[637,638],[573,1153,1154,1157],{"style":735},[573,1155],{"className":1156,"style":662},[661],[573,1158,1160],{"className":1159,"style":742},[674],[573,1161,1163],{"className":1162,"style":680},[679],[682,1164,1165],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1166],{"d":693},[573,1168,947],{"className":1169},[1000],[573,1171],{"className":1172,"style":698},[697],[573,1174,1089],{"className":1175},[702],[573,1177],{"className":1178,"style":698},[697],[573,1180,1182,1185],{"className":1181},[628],[573,1183],{"className":1184,"style":960},[632],[573,1186,929],{"className":1187,"style":964},[637,638],[1054,1189,1190],{},"leer, keine Lösung",[1039,1192,1193,1346],{},[1054,1194,1195],{},[573,1196,1198,1236],{"className":1197},[576],[573,1199,1201],{"className":1200},[580],[582,1202,1203],{"xmlns":584},[586,1204,1205,1233],{},[589,1206,1207,1209,1211,1213,1215,1217,1223,1225,1227,1229,1231],{},[592,1208,935],{"mathvariant":934},[603,1210,938],{},[603,1212,942],{"stretchy":941},[592,1214,594],{},[603,1216,1078],{},[596,1218,1219,1221],{"accent":598},[592,1220,613],{},[603,1222,605],{},[603,1224,947],{"stretchy":941},[603,1226,608],{},[592,1228,929],{},[603,1230,608],{},[592,1232,1016],{},[617,1234,1235],{"encoding":619},"\\operatorname{rg}(A \\mid \\vec b) = r = n",[573,1237,1239,1266,1319,1337],{"className":1238,"ariaHidden":598},[624],[573,1240,1242,1245,1251,1254,1257,1260,1263],{"className":1241},[628],[573,1243],{"className":1244,"style":980},[632],[573,1246,1248],{"className":1247},[984],[573,1249,935],{"className":1250,"style":989},[637,988],[573,1252,942],{"className":1253},[993],[573,1255,594],{"className":1256},[637,638],[573,1258],{"className":1259,"style":698},[697],[573,1261,1078],{"className":1262},[702],[573,1264],{"className":1265,"style":698},[697],[573,1267,1269,1272,1307,1310,1313,1316],{"className":1268},[628],[573,1270],{"className":1271,"style":1131},[632],[573,1273,1275],{"className":1274},[637,642],[573,1276,1278],{"className":1277},[646],[573,1279,1281],{"className":1280},[650],[573,1282,1284,1292],{"className":1283,"style":712},[654],[573,1285,1286,1289],{"style":657},[573,1287],{"className":1288,"style":662},[661],[573,1290,613],{"className":1291},[637,638],[573,1293,1294,1297],{"style":735},[573,1295],{"className":1296,"style":662},[661],[573,1298,1300],{"className":1299,"style":742},[674],[573,1301,1303],{"className":1302,"style":680},[679],[682,1304,1305],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1306],{"d":693},[573,1308,947],{"className":1309},[1000],[573,1311],{"className":1312,"style":698},[697],[573,1314,608],{"className":1315},[702],[573,1317],{"className":1318,"style":698},[697],[573,1320,1322,1325,1328,1331,1334],{"className":1321},[628],[573,1323],{"className":1324,"style":960},[632],[573,1326,929],{"className":1327,"style":964},[637,638],[573,1329],{"className":1330,"style":698},[697],[573,1332,608],{"className":1333},[702],[573,1335],{"className":1336,"style":698},[697],[573,1338,1340,1343],{"className":1339},[628],[573,1341],{"className":1342,"style":960},[632],[573,1344,1016],{"className":1345},[637,638],[1054,1347,1348],{},"genau eine Lösung",[1039,1350,1351,1506],{},[1054,1352,1353],{},[573,1354,1356,1395],{"className":1355},[576],[573,1357,1359],{"className":1358},[580],[582,1360,1361],{"xmlns":584},[586,1362,1363,1392],{},[589,1364,1365,1367,1369,1371,1373,1375,1381,1383,1385,1387,1390],{},[592,1366,935],{"mathvariant":934},[603,1368,938],{},[603,1370,942],{"stretchy":941},[592,1372,594],{},[603,1374,1078],{},[596,1376,1377,1379],{"accent":598},[592,1378,613],{},[603,1380,605],{},[603,1382,947],{"stretchy":941},[603,1384,608],{},[592,1386,929],{},[603,1388,1389],{},"\u003C",[592,1391,1016],{},[617,1393,1394],{"encoding":619},"\\operatorname{rg}(A \\mid \\vec b) = r \u003C n",[573,1396,1398,1425,1478,1497],{"className":1397,"ariaHidden":598},[624],[573,1399,1401,1404,1410,1413,1416,1419,1422],{"className":1400},[628],[573,1402],{"className":1403,"style":980},[632],[573,1405,1407],{"className":1406},[984],[573,1408,935],{"className":1409,"style":989},[637,988],[573,1411,942],{"className":1412},[993],[573,1414,594],{"className":1415},[637,638],[573,1417],{"className":1418,"style":698},[697],[573,1420,1078],{"className":1421},[702],[573,1423],{"className":1424,"style":698},[697],[573,1426,1428,1431,1466,1469,1472,1475],{"className":1427},[628],[573,1429],{"className":1430,"style":1131},[632],[573,1432,1434],{"className":1433},[637,642],[573,1435,1437],{"className":1436},[646],[573,1438,1440],{"className":1439},[650],[573,1441,1443,1451],{"className":1442,"style":712},[654],[573,1444,1445,1448],{"style":657},[573,1446],{"className":1447,"style":662},[661],[573,1449,613],{"className":1450},[637,638],[573,1452,1453,1456],{"style":735},[573,1454],{"className":1455,"style":662},[661],[573,1457,1459],{"className":1458,"style":742},[674],[573,1460,1462],{"className":1461,"style":680},[679],[682,1463,1464],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1465],{"d":693},[573,1467,947],{"className":1468},[1000],[573,1470],{"className":1471,"style":698},[697],[573,1473,608],{"className":1474},[702],[573,1476],{"className":1477,"style":698},[697],[573,1479,1481,1485,1488,1491,1494],{"className":1480},[628],[573,1482],{"className":1483,"style":1484},[632],"height:0.5782em;vertical-align:-0.0391em;",[573,1486,929],{"className":1487,"style":964},[637,638],[573,1489],{"className":1490,"style":698},[697],[573,1492,1389],{"className":1493},[702],[573,1495],{"className":1496,"style":698},[697],[573,1498,1500,1503],{"className":1499},[628],[573,1501],{"className":1502,"style":960},[632],[573,1504,1016],{"className":1505},[637,638],[1054,1507,1508,1509,1564],{},"unendlich viele Lösungen, ",[573,1510,1512,1531],{"className":1511},[576],[573,1513,1515],{"className":1514},[580],[582,1516,1517],{"xmlns":584},[586,1518,1519,1528],{},[589,1520,1521,1523,1526],{},[592,1522,1016],{},[603,1524,1525],{},"−",[592,1527,929],{},[617,1529,1530],{"encoding":619},"n - r",[573,1532,1534,1555],{"className":1533,"ariaHidden":598},[624],[573,1535,1537,1541,1544,1548,1552],{"className":1536},[628],[573,1538],{"className":1539,"style":1540},[632],"height:0.6667em;vertical-align:-0.0833em;",[573,1542,1016],{"className":1543},[637,638],[573,1545],{"className":1546,"style":1547},[697],"margin-right:0.2222em;",[573,1549,1525],{"className":1550},[1551],"mbin",[573,1553],{"className":1554,"style":1547},[697],[573,1556,1558,1561],{"className":1557},[628],[573,1559],{"className":1560,"style":960},[632],[573,1562,929],{"className":1563,"style":964},[637,638]," freie Parameter",[565,1566,1567,1570,1571,1691,1692,1695],{},[569,1568,1569],{},"Struktur der Lösungsmenge:"," Ist ",[573,1572,1574,1597],{"className":1573},[576],[573,1575,1577],{"className":1576},[580],[582,1578,1579],{"xmlns":584},[586,1580,1581,1594],{},[589,1582,1583],{},[1584,1585,1586,1592],"msub",{},[596,1587,1588,1590],{"accent":598},[592,1589,601],{},[603,1591,605],{},[592,1593,565],{},[617,1595,1596],{"encoding":619},"\\vec x_p",[573,1598,1600],{"className":1599,"ariaHidden":598},[624],[573,1601,1603,1607],{"className":1602},[628],[573,1604],{"className":1605,"style":1606},[632],"height:1.0001em;vertical-align:-0.2861em;",[573,1608,1610,1645],{"className":1609},[637],[573,1611,1613],{"className":1612},[637,642],[573,1614,1616],{"className":1615},[646],[573,1617,1619],{"className":1618},[650],[573,1620,1622,1630],{"className":1621,"style":633},[654],[573,1623,1624,1627],{"style":657},[573,1625],{"className":1626,"style":662},[661],[573,1628,601],{"className":1629},[637,638],[573,1631,1632,1635],{"style":657},[573,1633],{"className":1634,"style":662},[661],[573,1636,1638],{"className":1637,"style":675},[674],[573,1639,1641],{"className":1640,"style":680},[679],[682,1642,1643],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1644],{"d":693},[573,1646,1649],{"className":1647},[1648],"msupsub",[573,1650,1653,1682],{"className":1651},[646,1652],"vlist-t2",[573,1654,1656,1677],{"className":1655},[650],[573,1657,1660],{"className":1658,"style":1659},[654],"height:0.1514em;",[573,1661,1663,1667],{"style":1662},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[573,1664],{"className":1665,"style":1666},[661],"height:2.7em;",[573,1668,1674],{"className":1669},[1670,1671,1672,1673],"sizing","reset-size6","size3","mtight",[573,1675,565],{"className":1676},[637,638,1673],[573,1678,1681],{"className":1679},[1680],"vlist-s","​",[573,1683,1685],{"className":1684},[650],[573,1686,1689],{"className":1687,"style":1688},[654],"height:0.2861em;",[573,1690],{}," irgendeine Lösung (eine ",[569,1693,1694],{},"partikuläre"," Lösung), dann sind alle Lösungen",[573,1697,1700],{"className":1698},[1699],"katex-display",[573,1701,1703,1777],{"className":1702},[576],[573,1704,1706],{"className":1705},[580],[582,1707,1709],{"xmlns":584,"display":1708},"block",[586,1710,1711,1774],{},[589,1712,1713,1719,1721,1731,1734,1745,1748,1751,1761,1764,1767,1769,1771],{},[596,1714,1715,1717],{"accent":598},[592,1716,601],{},[603,1718,605],{},[603,1720,608],{},[1584,1722,1723,1729],{},[596,1724,1725,1727],{"accent":598},[592,1726,601],{},[603,1728,605],{},[592,1730,565],{},[603,1732,1733],{},"+",[1584,1735,1736,1742],{},[596,1737,1738,1740],{"accent":598},[592,1739,601],{},[603,1741,605],{},[592,1743,1744],{},"h",[603,1746,1747],{"separator":598},",",[697,1749],{"width":1750},"2em",[1584,1752,1753,1759],{},[596,1754,1755,1757],{"accent":598},[592,1756,601],{},[603,1758,605],{},[592,1760,1744],{},[603,1762,1763],{},"∈",[592,1765,1766],{"mathvariant":934},"Kern",[603,1768,938],{},[592,1770,594],{},[592,1772,1773],{"mathvariant":934},".",[617,1775,1776],{"encoding":619},"\\vec x = \\vec x_p + \\vec x_h, \\qquad \\vec x_h \\in \\operatorname{Kern} A.",[573,1778,1780,1830,1917,2091],{"className":1779,"ariaHidden":598},[624],[573,1781,1783,1786,1821,1824,1827],{"className":1782},[628],[573,1784],{"className":1785,"style":633},[632],[573,1787,1789],{"className":1788},[637,642],[573,1790,1792],{"className":1791},[646],[573,1793,1795],{"className":1794},[650],[573,1796,1798,1806],{"className":1797,"style":633},[654],[573,1799,1800,1803],{"style":657},[573,1801],{"className":1802,"style":662},[661],[573,1804,601],{"className":1805},[637,638],[573,1807,1808,1811],{"style":657},[573,1809],{"className":1810,"style":662},[661],[573,1812,1814],{"className":1813,"style":675},[674],[573,1815,1817],{"className":1816,"style":680},[679],[682,1818,1819],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1820],{"d":693},[573,1822],{"className":1823,"style":698},[697],[573,1825,608],{"className":1826},[702],[573,1828],{"className":1829,"style":698},[697],[573,1831,1833,1836,1908,1911,1914],{"className":1832},[628],[573,1834],{"className":1835,"style":1606},[632],[573,1837,1839,1874],{"className":1838},[637],[573,1840,1842],{"className":1841},[637,642],[573,1843,1845],{"className":1844},[646],[573,1846,1848],{"className":1847},[650],[573,1849,1851,1859],{"className":1850,"style":633},[654],[573,1852,1853,1856],{"style":657},[573,1854],{"className":1855,"style":662},[661],[573,1857,601],{"className":1858},[637,638],[573,1860,1861,1864],{"style":657},[573,1862],{"className":1863,"style":662},[661],[573,1865,1867],{"className":1866,"style":675},[674],[573,1868,1870],{"className":1869,"style":680},[679],[682,1871,1872],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1873],{"d":693},[573,1875,1877],{"className":1876},[1648],[573,1878,1880,1900],{"className":1879},[646,1652],[573,1881,1883,1897],{"className":1882},[650],[573,1884,1886],{"className":1885,"style":1659},[654],[573,1887,1888,1891],{"style":1662},[573,1889],{"className":1890,"style":1666},[661],[573,1892,1894],{"className":1893},[1670,1671,1672,1673],[573,1895,565],{"className":1896},[637,638,1673],[573,1898,1681],{"className":1899},[1680],[573,1901,1903],{"className":1902},[650],[573,1904,1906],{"className":1905,"style":1688},[654],[573,1907],{},[573,1909],{"className":1910,"style":1547},[697],[573,1912,1733],{"className":1913},[1551],[573,1915],{"className":1916,"style":1547},[697],[573,1918,1920,1924,1998,2002,2006,2010,2082,2085,2088],{"className":1919},[628],[573,1921],{"className":1922,"style":1923},[632],"height:0.9084em;vertical-align:-0.1944em;",[573,1925,1927,1962],{"className":1926},[637],[573,1928,1930],{"className":1929},[637,642],[573,1931,1933],{"className":1932},[646],[573,1934,1936],{"className":1935},[650],[573,1937,1939,1947],{"className":1938,"style":633},[654],[573,1940,1941,1944],{"style":657},[573,1942],{"className":1943,"style":662},[661],[573,1945,601],{"className":1946},[637,638],[573,1948,1949,1952],{"style":657},[573,1950],{"className":1951,"style":662},[661],[573,1953,1955],{"className":1954,"style":675},[674],[573,1956,1958],{"className":1957,"style":680},[679],[682,1959,1960],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,1961],{"d":693},[573,1963,1965],{"className":1964},[1648],[573,1966,1968,1989],{"className":1967},[646,1652],[573,1969,1971,1986],{"className":1970},[650],[573,1972,1975],{"className":1973,"style":1974},[654],"height:0.3361em;",[573,1976,1977,1980],{"style":1662},[573,1978],{"className":1979,"style":1666},[661],[573,1981,1983],{"className":1982},[1670,1671,1672,1673],[573,1984,1744],{"className":1985},[637,638,1673],[573,1987,1681],{"className":1988},[1680],[573,1990,1992],{"className":1991},[650],[573,1993,1996],{"className":1994,"style":1995},[654],"height:0.15em;",[573,1997],{},[573,1999,1747],{"className":2000},[2001],"mpunct",[573,2003],{"className":2004,"style":2005},[697],"margin-right:2em;",[573,2007],{"className":2008,"style":2009},[697],"margin-right:0.1667em;",[573,2011,2013,2048],{"className":2012},[637],[573,2014,2016],{"className":2015},[637,642],[573,2017,2019],{"className":2018},[646],[573,2020,2022],{"className":2021},[650],[573,2023,2025,2033],{"className":2024,"style":633},[654],[573,2026,2027,2030],{"style":657},[573,2028],{"className":2029,"style":662},[661],[573,2031,601],{"className":2032},[637,638],[573,2034,2035,2038],{"style":657},[573,2036],{"className":2037,"style":662},[661],[573,2039,2041],{"className":2040,"style":675},[674],[573,2042,2044],{"className":2043,"style":680},[679],[682,2045,2046],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2047],{"d":693},[573,2049,2051],{"className":2050},[1648],[573,2052,2054,2074],{"className":2053},[646,1652],[573,2055,2057,2071],{"className":2056},[650],[573,2058,2060],{"className":2059,"style":1974},[654],[573,2061,2062,2065],{"style":1662},[573,2063],{"className":2064,"style":1666},[661],[573,2066,2068],{"className":2067},[1670,1671,1672,1673],[573,2069,1744],{"className":2070},[637,638,1673],[573,2072,1681],{"className":2073},[1680],[573,2075,2077],{"className":2076},[650],[573,2078,2080],{"className":2079,"style":1995},[654],[573,2081],{},[573,2083],{"className":2084,"style":698},[697],[573,2086,1763],{"className":2087},[702],[573,2089],{"className":2090,"style":698},[697],[573,2092,2094,2097,2103,2106,2109],{"className":2093},[628],[573,2095],{"className":2096,"style":907},[632],[573,2098,2100],{"className":2099},[984],[573,2101,1766],{"className":2102},[637,988],[573,2104],{"className":2105,"style":2009},[697],[573,2107,594],{"className":2108},[637,638],[573,2110,1773],{"className":2111},[637],[565,2113,2114,2115,2165,2166,2298,2299,2422],{},"Die Lösungsmenge ist also eine verschobene Kopie des Kerns, ein affiner Raum der Dimension ",[573,2116,2118,2135],{"className":2117},[576],[573,2119,2121],{"className":2120},[580],[582,2122,2123],{"xmlns":584},[586,2124,2125,2133],{},[589,2126,2127,2129,2131],{},[592,2128,1016],{},[603,2130,1525],{},[592,2132,929],{},[617,2134,1530],{"encoding":619},[573,2136,2138,2156],{"className":2137,"ariaHidden":598},[624],[573,2139,2141,2144,2147,2150,2153],{"className":2140},[628],[573,2142],{"className":2143,"style":1540},[632],[573,2145,1016],{"className":2146},[637,638],[573,2148],{"className":2149,"style":1547},[697],[573,2151,1525],{"className":2152},[1551],[573,2154],{"className":2155,"style":1547},[697],[573,2157,2159,2162],{"className":2158},[628],[573,2160],{"className":2161,"style":960},[632],[573,2163,929],{"className":2164,"style":964},[637,638],". Das homogene System ",[573,2167,2169,2199],{"className":2168},[576],[573,2170,2172],{"className":2171},[580],[582,2173,2174],{"xmlns":584},[586,2175,2176,2196],{},[589,2177,2178,2180,2186,2188],{},[592,2179,594],{},[596,2181,2182,2184],{"accent":598},[592,2183,601],{},[603,2185,605],{},[603,2187,608],{},[596,2189,2190,2194],{"accent":598},[2191,2192,2193],"mn",{},"0",[603,2195,605],{},[617,2197,2198],{"encoding":619},"A\\vec x = \\vec 0",[573,2200,2202,2255],{"className":2201,"ariaHidden":598},[624],[573,2203,2205,2208,2211,2246,2249,2252],{"className":2204},[628],[573,2206],{"className":2207,"style":633},[632],[573,2209,594],{"className":2210},[637,638],[573,2212,2214],{"className":2213},[637,642],[573,2215,2217],{"className":2216},[646],[573,2218,2220],{"className":2219},[650],[573,2221,2223,2231],{"className":2222,"style":633},[654],[573,2224,2225,2228],{"style":657},[573,2226],{"className":2227,"style":662},[661],[573,2229,601],{"className":2230},[637,638],[573,2232,2233,2236],{"style":657},[573,2234],{"className":2235,"style":662},[661],[573,2237,2239],{"className":2238,"style":675},[674],[573,2240,2242],{"className":2241,"style":680},[679],[682,2243,2244],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2245],{"d":693},[573,2247],{"className":2248,"style":698},[697],[573,2250,608],{"className":2251},[702],[573,2253],{"className":2254,"style":698},[697],[573,2256,2258,2262],{"className":2257},[628],[573,2259],{"className":2260,"style":2261},[632],"height:0.9274em;",[573,2263,2265],{"className":2264},[637,642],[573,2266,2268],{"className":2267},[646],[573,2269,2271],{"className":2270},[650],[573,2272,2274,2282],{"className":2273,"style":2261},[654],[573,2275,2276,2279],{"style":657},[573,2277],{"className":2278,"style":662},[661],[573,2280,2193],{"className":2281},[637],[573,2283,2285,2288],{"style":2284},"top:-3.2134em;",[573,2286],{"className":2287,"style":662},[661],[573,2289,2291],{"className":2290,"style":742},[674],[573,2292,2294],{"className":2293,"style":680},[679],[682,2295,2296],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2297],{"d":693}," ist immer lösbar (mit ",[573,2300,2302,2328],{"className":2301},[576],[573,2303,2305],{"className":2304},[580],[582,2306,2307],{"xmlns":584},[586,2308,2309,2325],{},[589,2310,2311,2317,2319],{},[596,2312,2313,2315],{"accent":598},[592,2314,601],{},[603,2316,605],{},[603,2318,608],{},[596,2320,2321,2323],{"accent":598},[2191,2322,2193],{},[603,2324,605],{},[617,2326,2327],{"encoding":619},"\\vec x = \\vec 0",[573,2329,2331,2381],{"className":2330,"ariaHidden":598},[624],[573,2332,2334,2337,2372,2375,2378],{"className":2333},[628],[573,2335],{"className":2336,"style":633},[632],[573,2338,2340],{"className":2339},[637,642],[573,2341,2343],{"className":2342},[646],[573,2344,2346],{"className":2345},[650],[573,2347,2349,2357],{"className":2348,"style":633},[654],[573,2350,2351,2354],{"style":657},[573,2352],{"className":2353,"style":662},[661],[573,2355,601],{"className":2356},[637,638],[573,2358,2359,2362],{"style":657},[573,2360],{"className":2361,"style":662},[661],[573,2363,2365],{"className":2364,"style":675},[674],[573,2366,2368],{"className":2367,"style":680},[679],[682,2369,2370],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2371],{"d":693},[573,2373],{"className":2374,"style":698},[697],[573,2376,608],{"className":2377},[702],[573,2379],{"className":2380,"style":698},[697],[573,2382,2384,2387],{"className":2383},[628],[573,2385],{"className":2386,"style":2261},[632],[573,2388,2390],{"className":2389},[637,642],[573,2391,2393],{"className":2392},[646],[573,2394,2396],{"className":2395},[650],[573,2397,2399,2407],{"className":2398,"style":2261},[654],[573,2400,2401,2404],{"style":657},[573,2402],{"className":2403,"style":662},[661],[573,2405,2193],{"className":2406},[637],[573,2408,2409,2412],{"style":2284},[573,2410],{"className":2411,"style":662},[661],[573,2413,2415],{"className":2414,"style":742},[674],[573,2416,2418],{"className":2417,"style":680},[679],[682,2419,2420],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2421],{"d":693},").",[565,2424,2425,2426,2454,2455,2560,2561,2604,2605,2669],{},"Für quadratisches ",[573,2427,2429,2442],{"className":2428},[576],[573,2430,2432],{"className":2431},[580],[582,2433,2434],{"xmlns":584},[586,2435,2436,2440],{},[589,2437,2438],{},[592,2439,594],{},[617,2441,594],{"encoding":619},[573,2443,2445],{"className":2444,"ariaHidden":598},[624],[573,2446,2448,2451],{"className":2447},[628],[573,2449],{"className":2450,"style":907},[632],[573,2452,594],{"className":2453},[637,638]," gilt: ",[573,2456,2458,2482],{"className":2457},[576],[573,2459,2461],{"className":2460},[580],[582,2462,2463],{"xmlns":584},[586,2464,2465,2479],{},[589,2466,2467,2470,2472,2474,2477],{},[592,2468,2469],{},"det",[603,2471,938],{},[592,2473,594],{},[603,2475,2476],{"mathvariant":934},"≠",[2191,2478,2193],{},[617,2480,2481],{"encoding":619},"\\det A \\neq 0",[573,2483,2485,2550],{"className":2484,"ariaHidden":598},[624],[573,2486,2488,2492,2495,2498,2501,2504,2547],{"className":2487},[628],[573,2489],{"className":2490,"style":2491},[632],"height:0.8889em;vertical-align:-0.1944em;",[573,2493,2469],{"className":2494},[984],[573,2496],{"className":2497,"style":2009},[697],[573,2499,594],{"className":2500},[637,638],[573,2502],{"className":2503,"style":698},[697],[573,2505,2507,2540,2544],{"className":2506},[702],[573,2508,2510],{"className":2509},[702],[573,2511,2514],{"className":2512},[637,2513],"vbox",[573,2515,2518],{"className":2516},[2517],"thinbox",[573,2519,2522,2525,2536],{"className":2520},[2521],"rlap",[573,2523],{"className":2524,"style":2491},[632],[573,2526,2529],{"className":2527},[2528],"inner",[573,2530,2532],{"className":2531},[637],[573,2533,2535],{"className":2534},[702],"",[573,2537],{"className":2538},[2539],"fix",[573,2541],{"className":2542},[697,2543],"nobreak",[573,2545,608],{"className":2546},[702],[573,2548],{"className":2549,"style":698},[697],[573,2551,2553,2557],{"className":2552},[628],[573,2554],{"className":2555,"style":2556},[632],"height:0.6444em;",[573,2558,2193],{"className":2559},[637]," ",[573,2562,2564,2585],{"className":2563},[576],[573,2565,2567],{"className":2566},[580],[582,2568,2569],{"xmlns":584},[586,2570,2571,2582],{},[589,2572,2573,2577,2580],{},[2574,2575,2576],"mtext",{},"  ",[603,2578,2579],{},"⟺",[2574,2581,2576],{},[617,2583,2584],{"encoding":619},"\\iff",[573,2586,2588],{"className":2587,"ariaHidden":598},[624],[573,2589,2591,2595,2598,2601],{"className":2590},[628],[573,2592],{"className":2593,"style":2594},[632],"height:0.549em;vertical-align:-0.024em;",[573,2596],{"className":2597,"style":698},[697],[573,2599,2579],{"className":2600},[702],[573,2602],{"className":2603,"style":698},[697]," für jedes ",[573,2606,2608,2625],{"className":2607},[576],[573,2609,2611],{"className":2610},[580],[582,2612,2613],{"xmlns":584},[586,2614,2615,2623],{},[589,2616,2617],{},[596,2618,2619,2621],{"accent":598},[592,2620,613],{},[603,2622,605],{},[617,2624,771],{"encoding":619},[573,2626,2628],{"className":2627,"ariaHidden":598},[624],[573,2629,2631,2634],{"className":2630},[628],[573,2632],{"className":2633,"style":712},[632],[573,2635,2637],{"className":2636},[637,642],[573,2638,2640],{"className":2639},[646],[573,2641,2643],{"className":2642},[650],[573,2644,2646,2654],{"className":2645,"style":712},[654],[573,2647,2648,2651],{"style":657},[573,2649],{"className":2650,"style":662},[661],[573,2652,613],{"className":2653},[637,638],[573,2655,2656,2659],{"style":735},[573,2657],{"className":2658,"style":662},[661],[573,2660,2662],{"className":2661,"style":742},[674],[573,2663,2665],{"className":2664,"style":680},[679],[682,2666,2667],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2668],{"d":693}," genau eine Lösung.",[565,2671,2672,2673,2770,2771,2862,2863,2947,2948,1773],{},"In der Praxis bringt man ",[573,2674,2676,2702],{"className":2675},[576],[573,2677,2679],{"className":2678},[580],[582,2680,2681],{"xmlns":584},[586,2682,2683,2699],{},[589,2684,2685,2687,2689,2691,2697],{},[603,2686,942],{"stretchy":941},[592,2688,594],{},[603,2690,1078],{},[596,2692,2693,2695],{"accent":598},[592,2694,613],{},[603,2696,605],{},[603,2698,947],{"stretchy":941},[617,2700,2701],{"encoding":619},"(A \\mid \\vec b)",[573,2703,2705,2726],{"className":2704,"ariaHidden":598},[624],[573,2706,2708,2711,2714,2717,2720,2723],{"className":2707},[628],[573,2709],{"className":2710,"style":980},[632],[573,2712,942],{"className":2713},[993],[573,2715,594],{"className":2716},[637,638],[573,2718],{"className":2719,"style":698},[697],[573,2721,1078],{"className":2722},[702],[573,2724],{"className":2725,"style":698},[697],[573,2727,2729,2732,2767],{"className":2728},[628],[573,2730],{"className":2731,"style":1131},[632],[573,2733,2735],{"className":2734},[637,642],[573,2736,2738],{"className":2737},[646],[573,2739,2741],{"className":2740},[650],[573,2742,2744,2752],{"className":2743,"style":712},[654],[573,2745,2746,2749],{"style":657},[573,2747],{"className":2748,"style":662},[661],[573,2750,613],{"className":2751},[637,638],[573,2753,2754,2757],{"style":735},[573,2755],{"className":2756,"style":662},[661],[573,2758,2760],{"className":2759,"style":742},[674],[573,2761,2763],{"className":2762,"style":680},[679],[682,2764,2765],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,2766],{"d":693},[573,2768,947],{"className":2769},[1000]," mit dem Gauß-Algorithmus auf Stufenform. Eine Zeile ",[573,2772,2774,2807],{"className":2773},[576],[573,2775,2777],{"className":2776},[580],[582,2778,2779],{"xmlns":584},[586,2780,2781,2804],{},[589,2782,2783,2785,2787,2790,2793,2795,2797,2799,2802],{},[603,2784,942],{"stretchy":941},[2191,2786,2193],{},[2574,2788,2789],{}," ",[603,2791,2792],{},"⋯",[2574,2794,2789],{},[2191,2796,2193],{},[603,2798,1078],{},[592,2800,2801],{},"c",[603,2803,947],{"stretchy":941},[617,2805,2806],{"encoding":619},"(0 \\ \\cdots \\ 0 \\mid c)",[573,2808,2810,2850],{"className":2809,"ariaHidden":598},[624],[573,2811,2813,2816,2819,2822,2825,2828,2832,2835,2838,2841,2844,2847],{"className":2812},[628],[573,2814],{"className":2815,"style":980},[632],[573,2817,942],{"className":2818},[993],[573,2820,2193],{"className":2821},[637],[573,2823,2789],{"className":2824},[697],[573,2826],{"className":2827,"style":2009},[697],[573,2829,2792],{"className":2830},[2831],"minner",[573,2833,2789],{"className":2834},[697],[573,2836],{"className":2837,"style":2009},[697],[573,2839,2193],{"className":2840},[637],[573,2842],{"className":2843,"style":698},[697],[573,2845,1078],{"className":2846},[702],[573,2848],{"className":2849,"style":698},[697],[573,2851,2853,2856,2859],{"className":2852},[628],[573,2854],{"className":2855,"style":980},[632],[573,2857,2801],{"className":2858},[637,638],[573,2860,947],{"className":2861},[1000]," mit ",[573,2864,2866,2884],{"className":2865},[576],[573,2867,2869],{"className":2868},[580],[582,2870,2871],{"xmlns":584},[586,2872,2873,2881],{},[589,2874,2875,2877,2879],{},[592,2876,2801],{},[603,2878,2476],{"mathvariant":934},[2191,2880,2193],{},[617,2882,2883],{"encoding":619},"c \\neq 0",[573,2885,2887,2938],{"className":2886,"ariaHidden":598},[624],[573,2888,2890,2893,2896,2899,2935],{"className":2889},[628],[573,2891],{"className":2892,"style":2491},[632],[573,2894,2801],{"className":2895},[637,638],[573,2897],{"className":2898,"style":698},[697],[573,2900,2902,2929,2932],{"className":2901},[702],[573,2903,2905],{"className":2904},[702],[573,2906,2908],{"className":2907},[637,2513],[573,2909,2911],{"className":2910},[2517],[573,2912,2914,2917,2926],{"className":2913},[2521],[573,2915],{"className":2916,"style":2491},[632],[573,2918,2920],{"className":2919},[2528],[573,2921,2923],{"className":2922},[637],[573,2924,2535],{"className":2925},[702],[573,2927],{"className":2928},[2539],[573,2930],{"className":2931},[697,2543],[573,2933,608],{"className":2934},[702],[573,2936],{"className":2937,"style":698},[697],[573,2939,2941,2944],{"className":2940},[628],[573,2942],{"className":2943,"style":2556},[632],[573,2945,2193],{"className":2946},[637]," bedeutet ",[573,2949,2951,2993],{"className":2950},[576],[573,2952,2954],{"className":2953},[580],[582,2955,2956],{"xmlns":584},[586,2957,2958,2990],{},[589,2959,2960,2962,2964,2966,2968,2970,2976,2978,2980,2982,2984,2986,2988],{},[592,2961,935],{"mathvariant":934},[603,2963,938],{},[603,2965,942],{"stretchy":941},[592,2967,594],{},[603,2969,1078],{},[596,2971,2972,2974],{"accent":598},[592,2973,613],{},[603,2975,605],{},[603,2977,947],{"stretchy":941},[603,2979,1089],{},[592,2981,935],{"mathvariant":934},[603,2983,938],{},[603,2985,942],{"stretchy":941},[592,2987,594],{},[603,2989,947],{"stretchy":941},[617,2991,2992],{"encoding":619},"\\operatorname{rg}(A \\mid \\vec b) > 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ist die Lösungsmenge ",[573,4703,4705,4758],{"className":4704},[576],[573,4706,4708],{"className":4707},[580],[582,4709,4710],{"xmlns":584},[586,4711,4712,4755],{},[589,4713,4714,4717,4719,4721,4723,4725,4727,4729,4731,4733,4735,4737,4739,4741,4744,4746,4748,4752],{},[603,4715,4716],{"stretchy":941},"{",[603,4718,942],{"stretchy":941},[2191,4720,3154],{},[603,4722,1525],{},[2191,4724,3161],{},[592,4726,4629],{},[603,4728,1747],{"separator":598},[2574,4730,2789],{},[592,4732,4629],{},[603,4734,1747],{"separator":598},[2574,4736,2789],{},[2191,4738,3154],{},[603,4740,947],{"stretchy":941},[603,4742,4743],{},":",[592,4745,4629],{},[603,4747,1763],{},[592,4749,4751],{"mathvariant":4750},"double-struck","R",[603,4753,4754],{"stretchy":941},"}",[617,4756,4757],{"encoding":619},"\\{(1 - 2t,\\ t,\\ 1) : t \\in 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Dann ist ",[573,5346,5348,5398],{"className":5347},[576],[573,5349,5351],{"className":5350},[580],[582,5352,5353],{"xmlns":584},[586,5354,5355,5395],{},[589,5356,5357,5359,5361,5363,5365,5367,5373,5375,5377,5379,5381,5383,5385,5387,5389,5391,5393],{},[592,5358,935],{"mathvariant":934},[603,5360,938],{},[603,5362,942],{"stretchy":941},[592,5364,594],{},[603,5366,1078],{},[596,5368,5369,5371],{"accent":598},[592,5370,613],{},[603,5372,605],{},[603,5374,947],{"stretchy":941},[603,5376,608],{},[2191,5378,3209],{},[603,5380,1089],{},[2191,5382,3161],{},[603,5384,608],{},[592,5386,935],{"mathvariant":934},[603,5388,938],{},[603,5390,942],{"stretchy":941},[592,5392,594],{},[603,5394,947],{"stretchy":941},[617,5396,5397],{"encoding":619},"\\operatorname{rg}(A \\mid \\vec b) = 3 > 2 = \\operatorname{rg}(A)",[573,5399,5401,5428,5481,5500,5518],{"className":5400,"ariaHidden":598},[624],[573,5402,5404,5407,5413,5416,5419,5422,5425],{"className":5403},[628],[573,5405],{"className":5406,"style":980},[632],[573,5408,5410],{"className":5409},[984],[573,5411,935],{"className":5412,"style":989},[637,988],[573,5414,942],{"className":5415},[993],[573,5417,594],{"className":5418},[637,638],[573,5420],{"className":5421,"style":698},[697],[573,5423,1078],{"className":5424},[702],[573,5426],{"className":5427,"style":698},[697],[573,5429,5431,5434,5469,5472,5475,5478],{"className":5430},[628],[573,5432],{"className":5433,"style":1131},[632],[573,5435,5437],{"className":5436},[637,642],[573,5438,5440],{"className":5439},[646],[573,5441,5443],{"className":5442},[650],[573,5444,5446,5454],{"className":5445,"style":712},[654],[573,5447,5448,5451],{"style":657},[573,5449],{"className":5450,"style":662},[661],[573,5452,613],{"className":5453},[637,638],[573,5455,5456,5459],{"style":735},[573,5457],{"className":5458,"style":662},[661],[573,5460,5462],{"className":5461,"style":742},[674],[573,5463,5465],{"className":5464,"style":680},[679],[682,5466,5467],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,5468],{"d":693},[573,5470,947],{"className":5471},[1000],[573,5473],{"className":5474,"style":698},[697],[573,5476,608],{"className":5477},[702],[573,5479],{"className":5480,"style":698},[697],[573,5482,5484,5488,5491,5494,5497],{"className":5483},[628],[573,5485],{"className":5486,"style":5487},[632],"height:0.6835em;vertical-align:-0.0391em;",[573,5489,3209],{"className":5490},[637],[573,5492],{"className":5493,"style":698},[697],[573,5495,1089],{"className":5496},[702],[573,5498],{"className":5499,"style":698},[697],[573,5501,5503,5506,5509,5512,5515],{"className":5502},[628],[573,5504],{"className":5505,"style":2556},[632],[573,5507,3161],{"className":5508},[637],[573,5510],{"className":5511,"style":698},[697],[573,5513,608],{"className":5514},[702],[573,5516],{"className":5517,"style":698},[697],[573,5519,5521,5524,5530,5533,5536],{"className":5520},[628],[573,5522],{"className":5523,"style":980},[632],[573,5525,5527],{"className":5526},[984],[573,5528,935],{"className":5529,"style":989},[637,988],[573,5531,942],{"className":5532},[993],[573,5534,594],{"className":5535},[637,638],[573,5537,947],{"className":5538},[1000],", das System hat keine Lösung.",[565,5541,5542,5543,5619,5620,5693,5694,4863,5978,6071,6072,1773],{},"Das System ",[573,5544,5546,5569],{"className":5545},[576],[573,5547,5549],{"className":5548},[580],[582,5550,5551],{"xmlns":584},[586,5552,5553,5566],{},[589,5554,5555,5557,5559,5562,5564],{},[592,5556,601],{},[603,5558,1733],{},[592,5560,5561],{},"y",[603,5563,608],{},[2191,5565,5157],{},[617,5567,5568],{"encoding":619},"x + y = 5",[573,5570,5572,5590,5610],{"className":5571,"ariaHidden":598},[624],[573,5573,5575,5578,5581,5584,5587],{"className":5574},[628],[573,5576],{"className":5577,"style":1540},[632],[573,5579,601],{"className":5580},[637,638],[573,5582],{"className":5583,"style":1547},[697],[573,5585,1733],{"className":5586},[1551],[573,5588],{"className":5589,"style":1547},[697],[573,5591,5593,5597,5601,5604,5607],{"className":5592},[628],[573,5594],{"className":5595,"style":5596},[632],"height:0.625em;vertical-align:-0.1944em;",[573,5598,5561],{"className":5599,"style":5600},[637,638],"margin-right:0.0359em;",[573,5602],{"className":5603,"style":698},[697],[573,5605,608],{"className":5606},[702],[573,5608],{"className":5609,"style":698},[697],[573,5611,5613,5616],{"className":5612},[628],[573,5614],{"className":5615,"style":2556},[632],[573,5617,5157],{"className":5618},[637],", ",[573,5621,5623,5645],{"className":5622},[576],[573,5624,5626],{"className":5625},[580],[582,5627,5628],{"xmlns":584},[586,5629,5630,5642],{},[589,5631,5632,5634,5636,5638,5640],{},[592,5633,601],{},[603,5635,1525],{},[592,5637,5561],{},[603,5639,608],{},[2191,5641,3154],{},[617,5643,5644],{"encoding":619},"x - y = 1",[573,5646,5648,5666,5684],{"className":5647,"ariaHidden":598},[624],[573,5649,5651,5654,5657,5660,5663],{"className":5650},[628],[573,5652],{"className":5653,"style":1540},[632],[573,5655,601],{"className":5656},[637,638],[573,5658],{"className":5659,"style":1547},[697],[573,5661,1525],{"className":5662},[1551],[573,5664],{"className":5665,"style":1547},[697],[573,5667,5669,5672,5675,5678,5681],{"className":5668},[628],[573,5670],{"className":5671,"style":5596},[632],[573,5673,5561],{"className":5674,"style":5600},[637,638],[573,5676],{"className":5677,"style":698},[697],[573,5679,608],{"className":5680},[702],[573,5682],{"className":5683,"style":698},[697],[573,5685,5687,5690],{"className":5686},[628],[573,5688],{"className":5689,"style":2556},[632],[573,5691,3154],{"className":5692},[637]," hat ",[573,5695,5697,5764],{"className":5696},[576],[573,5698,5700],{"className":5699},[580],[582,5701,5702],{"xmlns":584},[586,5703,5704,5761],{},[589,5705,5706,5708,5710,5751,5753,5755,5757,5759],{},[592,5707,2469],{},[603,5709,938],{},[589,5711,5712,5714,5749],{},[603,5713,942],{"fence":598},[3137,5715,5717,5731],{"rowspacing":3139,"columnalign":5716,"columnspacing":3142},"center center",[3144,5718,5719,5725],{},[3147,5720,5721],{},[3150,5722,5723],{"scriptlevel":2193,"displaystyle":941},[2191,5724,3154],{},[3147,5726,5727],{},[3150,5728,5729],{"scriptlevel":2193,"displaystyle":941},[2191,5730,3154],{},[3144,5732,5733,5739],{},[3147,5734,5735],{},[3150,5736,5737],{"scriptlevel":2193,"displaystyle":941},[2191,5738,3154],{},[3147,5740,5741],{},[3150,5742,5743],{"scriptlevel":2193,"displaystyle":941},[589,5744,5745,5747],{},[603,5746,1525],{},[2191,5748,3154],{},[603,5750,947],{"fence":598},[603,5752,608],{},[603,5754,1525],{},[2191,5756,3161],{},[603,5758,2476],{"mathvariant":934},[2191,5760,2193],{},[617,5762,5763],{"encoding":619},"\\det \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} = -2 \\neq 0",[573,5765,5767,5915,5969],{"className":5766,"ariaHidden":598},[624],[573,5768,5770,5774,5777,5780,5906,5909,5912],{"className":5769},[628],[573,5771],{"className":5772,"style":5773},[632],"height:2.4em;vertical-align:-0.95em;",[573,5775,2469],{"className":5776},[984],[573,5778],{"className":5779,"style":2009},[697],[573,5781,5783,5791,5900],{"className":5782},[2831],[573,5784,5788],{"className":5785,"style":5787},[993,5786],"delimcenter","top:0em;",[573,5789,942],{"className":5790},[3428,1672],[573,5792,5794],{"className":5793},[637],[573,5795,5797,5846,5849,5852],{"className":5796},[3137],[573,5798,5800],{"className":5799},[3484],[573,5801,5803,5837],{"className":5802},[646,1652],[573,5804,5806,5834],{"className":5805},[650],[573,5807,5810,5822],{"className":5808,"style":5809},[654],"height:1.45em;",[573,5811,5813,5816],{"style":5812},"top:-3.61em;",[573,5814],{"className":5815,"style":662},[661],[573,5817,5819],{"className":5818},[637],[573,5820,3154],{"className":5821},[637],[573,5823,5825,5828],{"style":5824},"top:-2.41em;",[573,5826],{"className":5827,"style":662},[661],[573,5829,5831],{"className":5830},[637],[573,5832,3154],{"className":5833},[637],[573,5835,1681],{"className":5836},[1680],[573,5838,5840],{"className":5839},[650],[573,5841,5844],{"className":5842,"style":5843},[654],"height:0.95em;",[573,5845],{},[573,5847],{"className":5848,"style":3480},[3479],[573,5850],{"className":5851,"style":3480},[3479],[573,5853,5855],{"className":5854},[3484],[573,5856,5858,5892],{"className":5857},[646,1652],[573,5859,5861,5889],{"className":5860},[650],[573,5862,5864,5875],{"className":5863,"style":5809},[654],[573,5865,5866,5869],{"style":5812},[573,5867],{"className":5868,"style":662},[661],[573,5870,5872],{"className":5871},[637],[573,5873,3154],{"className":5874},[637],[573,5876,5877,5880],{"style":5824},[573,5878],{"className":5879,"style":662},[661],[573,5881,5883,5886],{"className":5882},[637],[573,5884,1525],{"className":5885},[637],[573,5887,3154],{"className":5888},[637],[573,5890,1681],{"className":5891},[1680],[573,5893,5895],{"className":5894},[650],[573,5896,5898],{"className":5897,"style":5843},[654],[573,5899],{},[573,5901,5903],{"className":5902,"style":5787},[1000,5786],[573,5904,947],{"className":5905},[3428,1672],[573,5907],{"className":5908,"style":698},[697],[573,5910,608],{"className":5911},[702],[573,5913],{"className":5914,"style":698},[697],[573,5916,5918,5921,5924,5927,5930,5966],{"className":5917},[628],[573,5919],{"className":5920,"style":2491},[632],[573,5922,1525],{"className":5923},[637],[573,5925,3161],{"className":5926},[637],[573,5928],{"className":5929,"style":698},[697],[573,5931,5933,5960,5963],{"className":5932},[702],[573,5934,5936],{"className":5935},[702],[573,5937,5939],{"className":5938},[637,2513],[573,5940,5942],{"className":5941},[2517],[573,5943,5945,5948,5957],{"className":5944},[2521],[573,5946],{"className":5947,"style":2491},[632],[573,5949,5951],{"className":5950},[2528],[573,5952,5954],{"className":5953},[637],[573,5955,2535],{"className":5956},[702],[573,5958],{"className":5959},[2539],[573,5961],{"className":5962},[697,2543],[573,5964,608],{"className":5965},[702],[573,5967],{"className":5968,"style":698},[697],[573,5970,5972,5975],{"className":5971},[628],[573,5973],{"className":5974,"style":2556},[632],[573,5976,2193],{"className":5977},[637],[573,5979,5981,6011],{"className":5980},[576],[573,5982,5984],{"className":5983},[580],[582,5985,5986],{"xmlns":584},[586,5987,5988,6008],{},[589,5989,5990,5992,5994,5996,5998,6000,6002,6004,6006],{},[592,5991,935],{"mathvariant":934},[603,5993,938],{},[603,5995,942],{"stretchy":941},[592,5997,594],{},[603,5999,947],{"stretchy":941},[603,6001,608],{},[2191,6003,3161],{},[603,6005,608],{},[592,6007,1016],{},[617,6009,6010],{"encoding":619},"\\operatorname{rg}(A) = 2 = n",[573,6012,6014,6044,6062],{"className":6013,"ariaHidden":598},[624],[573,6015,6017,6020,6026,6029,6032,6035,6038,6041],{"className":6016},[628],[573,6018],{"className":6019,"style":980},[632],[573,6021,6023],{"className":6022},[984],[573,6024,935],{"className":6025,"style":989},[637,988],[573,6027,942],{"className":6028},[993],[573,6030,594],{"className":6031},[637,638],[573,6033,947],{"className":6034},[1000],[573,6036],{"className":6037,"style":698},[697],[573,6039,608],{"className":6040},[702],[573,6042],{"className":6043,"style":698},[697],[573,6045,6047,6050,6053,6056,6059],{"className":6046},[628],[573,6048],{"className":6049,"style":2556},[632],[573,6051,3161],{"className":6052},[637],[573,6054],{"className":6055,"style":698},[697],[573,6057,608],{"className":6058},[702],[573,6060],{"className":6061,"style":698},[697],[573,6063,6065,6068],{"className":6064},[628],[573,6066],{"className":6067,"style":960},[632],[573,6069,1016],{"className":6070},[637,638]," und genau eine Lösung: ",[573,6073,6075,6099],{"className":6074},[576],[573,6076,6078],{"className":6077},[580],[582,6079,6080],{"xmlns":584},[586,6081,6082,6096],{},[589,6083,6084,6086,6088,6090,6092,6094],{},[603,6085,942],{"stretchy":941},[2191,6087,3209],{},[603,6089,1747],{"separator":598},[2574,6091,2789],{},[2191,6093,3161],{},[603,6095,947],{"stretchy":941},[617,6097,6098],{"encoding":619},"(3,\\ 2)",[573,6100,6102],{"className":6101,"ariaHidden":598},[624],[573,6103,6105,6108,6111,6114,6117,6120,6123,6126],{"className":6104},[628],[573,6106],{"className":6107,"style":980},[632],[573,6109,942],{"className":6110},[993],[573,6112,3209],{"className":6113},[637],[573,6115,1747],{"className":6116},[2001],[573,6118,2789],{"className":6119},[697],[573,6121],{"className":6122,"style":2009},[697],[573,6124,3161],{"className":6125},[637],[573,6127,947],{"className":6128},[1000],[560,6130,6132],{"id":6131},"typische-fehler","Typische Fehler",[6134,6135,6136,6277,6384],"ul",{},[6137,6138,6139,6140,6168,6169,6276],"li",{},"Nur den Rang von ",[573,6141,6143,6156],{"className":6142},[576],[573,6144,6146],{"className":6145},[580],[582,6147,6148],{"xmlns":584},[586,6149,6150,6154],{},[589,6151,6152],{},[592,6153,594],{},[617,6155,594],{"encoding":619},[573,6157,6159],{"className":6158,"ariaHidden":598},[624],[573,6160,6162,6165],{"className":6161},[628],[573,6163],{"className":6164,"style":907},[632],[573,6166,594],{"className":6167},[637,638]," bestimmen und die rechte Seite ignorieren. Erst der Vergleich mit ",[573,6170,6172,6202],{"className":6171},[576],[573,6173,6175],{"className":6174},[580],[582,6176,6177],{"xmlns":584},[586,6178,6179,6199],{},[589,6180,6181,6183,6185,6187,6189,6191,6197],{},[592,6182,935],{"mathvariant":934},[603,6184,938],{},[603,6186,942],{"stretchy":941},[592,6188,594],{},[603,6190,1078],{},[596,6192,6193,6195],{"accent":598},[592,6194,613],{},[603,6196,605],{},[603,6198,947],{"stretchy":941},[617,6200,6201],{"encoding":619},"\\operatorname{rg}(A \\mid \\vec b)",[573,6203,6205,6232],{"className":6204,"ariaHidden":598},[624],[573,6206,6208,6211,6217,6220,6223,6226,6229],{"className":6207},[628],[573,6209],{"className":6210,"style":980},[632],[573,6212,6214],{"className":6213},[984],[573,6215,935],{"className":6216,"style":989},[637,988],[573,6218,942],{"className":6219},[993],[573,6221,594],{"className":6222},[637,638],[573,6224],{"className":6225,"style":698},[697],[573,6227,1078],{"className":6228},[702],[573,6230],{"className":6231,"style":698},[697],[573,6233,6235,6238,6273],{"className":6234},[628],[573,6236],{"className":6237,"style":1131},[632],[573,6239,6241],{"className":6240},[637,642],[573,6242,6244],{"className":6243},[646],[573,6245,6247],{"className":6246},[650],[573,6248,6250,6258],{"className":6249,"style":712},[654],[573,6251,6252,6255],{"style":657},[573,6253],{"className":6254,"style":662},[661],[573,6256,613],{"className":6257},[637,638],[573,6259,6260,6263],{"style":735},[573,6261],{"className":6262,"style":662},[661],[573,6264,6266],{"className":6265,"style":742},[674],[573,6267,6269],{"className":6268,"style":680},[679],[682,6270,6271],{"xmlns":684,"width":685,"height":686,"style":687,"viewBox":688,"preserveAspectRatio":689},[691,6272],{"d":693},[573,6274,947],{"className":6275},[1000]," entscheidet über die Lösbarkeit.",[6137,6278,6279,6280,6332,6333,6383],{},"Die Zahl der freien Parameter als ",[573,6281,6283,6302],{"className":6282},[576],[573,6284,6286],{"className":6285},[580],[582,6287,6288],{"xmlns":584},[586,6289,6290,6299],{},[589,6291,6292,6295,6297],{},[592,6293,6294],{},"m",[603,6296,1525],{},[592,6298,929],{},[617,6300,6301],{"encoding":619},"m - r",[573,6303,6305,6323],{"className":6304,"ariaHidden":598},[624],[573,6306,6308,6311,6314,6317,6320],{"className":6307},[628],[573,6309],{"className":6310,"style":1540},[632],[573,6312,6294],{"className":6313},[637,638],[573,6315],{"className":6316,"style":1547},[697],[573,6318,1525],{"className":6319},[1551],[573,6321],{"className":6322,"style":1547},[697],[573,6324,6326,6329],{"className":6325},[628],[573,6327],{"className":6328,"style":960},[632],[573,6330,929],{"className":6331,"style":964},[637,638]," (Gleichungen minus Rang) statt ",[573,6334,6336,6353],{"className":6335},[576],[573,6337,6339],{"className":6338},[580],[582,6340,6341],{"xmlns":584},[586,6342,6343,6351],{},[589,6344,6345,6347,6349],{},[592,6346,1016],{},[603,6348,1525],{},[592,6350,929],{},[617,6352,1530],{"encoding":619},[573,6354,6356,6374],{"className":6355,"ariaHidden":598},[624],[573,6357,6359,6362,6365,6368,6371],{"className":6358},[628],[573,6360],{"className":6361,"style":1540},[632],[573,6363,1016],{"className":6364},[637,638],[573,6366],{"className":6367,"style":1547},[697],[573,6369,1525],{"className":6370},[1551],[573,6372],{"className":6373,"style":1547},[697],[573,6375,6377,6380],{"className":6376},[628],[573,6378],{"className":6379,"style":960},[632],[573,6381,929],{"className":6382,"style":964},[637,638]," (Unbekannte minus Rang) berechnen.",[6137,6385,6386,6387,5619,6485,1773],{},"Aus „mehr Unbekannte als Gleichungen\" auf unendlich viele Lösungen schließen. Das System kann trotzdem widersprüchlich sein, z.B. ",[573,6388,6390,6417],{"className":6389},[576],[573,6391,6393],{"className":6392},[580],[582,6394,6395],{"xmlns":584},[586,6396,6397,6414],{},[589,6398,6399,6401,6403,6405,6407,6410,6412],{},[592,6400,601],{},[603,6402,1733],{},[592,6404,5561],{},[603,6406,1733],{},[592,6408,6409],{},"z",[603,6411,608],{},[2191,6413,3154],{},[617,6415,6416],{"encoding":619},"x + y + z = 1",[573,6418,6420,6438,6457,6476],{"className":6419,"ariaHidden":598},[624],[573,6421,6423,6426,6429,6432,6435],{"className":6422},[628],[573,6424],{"className":6425,"style":1540},[632],[573,6427,601],{"className":6428},[637,638],[573,6430],{"className":6431,"style":1547},[697],[573,6433,1733],{"className":6434},[1551],[573,6436],{"className":6437,"style":1547},[697],[573,6439,6441,6445,6448,6451,6454],{"className":6440},[628],[573,6442],{"className":6443,"style":6444},[632],"height:0.7778em;vertical-align:-0.1944em;",[573,6446,5561],{"className":6447,"style":5600},[637,638],[573,6449],{"className":6450,"style":1547},[697],[573,6452,1733],{"className":6453},[1551],[573,6455],{"className":6456,"style":1547},[697],[573,6458,6460,6463,6467,6470,6473],{"className":6459},[628],[573,6461],{"className":6462,"style":960},[632],[573,6464,6409],{"className":6465,"style":6466},[637,638],"margin-right:0.044em;",[573,6468],{"className":6469,"style":698},[697],[573,6471,608],{"className":6472},[702],[573,6474],{"className":6475,"style":698},[697],[573,6477,6479,6482],{"className":6478},[628],[573,6480],{"className":6481,"style":2556},[632],[573,6483,3154],{"className":6484},[637],[573,6486,6488,6514],{"className":6487},[576],[573,6489,6491],{"className":6490},[580],[582,6492,6493],{"xmlns":584},[586,6494,6495,6511],{},[589,6496,6497,6499,6501,6503,6505,6507,6509],{},[592,6498,601],{},[603,6500,1733],{},[592,6502,5561],{},[603,6504,1733],{},[592,6506,6409],{},[603,6508,608],{},[2191,6510,3161],{},[617,6512,6513],{"encoding":619},"x + y + z = 2",[573,6515,6517,6535,6553,6571],{"className":6516,"ariaHidden":598},[624],[573,6518,6520,6523,6526,6529,6532],{"className":6519},[628],[573,6521],{"className":6522,"style":1540},[632],[573,6524,601],{"className":6525},[637,638],[573,6527],{"className":6528,"style":1547},[697],[573,6530,1733],{"className":6531},[1551],[573,6533],{"className":6534,"style":1547},[697],[573,6536,6538,6541,6544,6547,6550],{"className":6537},[628],[573,6539],{"className":6540,"style":6444},[632],[573,6542,5561],{"className":6543,"style":5600},[637,638],[573,6545],{"className":6546,"style":1547},[697],[573,6548,1733],{"className":6549},[1551],[573,6551],{"className":6552,"style":1547},[697],[573,6554,6556,6559,6562,6565,6568],{"className":6555},[628],[573,6557],{"className":6558,"style":960},[632],[573,6560,6409],{"className":6561,"style":6466},[637,638],[573,6563],{"className":6564,"style":698},[697],[573,6566,608],{"className":6567},[702],[573,6569],{"className":6570,"style":698},[697],[573,6572,6574,6577],{"className":6573},[628],[573,6575],{"className":6576,"style":2556},[632],[573,6578,3161],{"className":6579},[637],{"title":6581,"searchDepth":6582,"depth":6582,"links":6583},"",2,[6584,6585,6586],{"id":562,"depth":6582,"text":563},{"id":3099,"depth":6582,"text":3100},{"id":6131,"depth":6582,"text":6132},[6588,6590,6592,6594,6597,6599,6601,6603,6605,6608,6610,6612,6616],{"lhs":6589,"rhs":3161},"(1 - 2*t) + 2*t + 1",{"lhs":6591,"rhs":3161},"2*(1 - 2*t) + 4*t + 0*1",{"lhs":6593,"rhs":3188},"3*(1 - 2*t) + 6*t + 1",{"lhs":6595,"rhs":6596},"2 - 2*2","-2",{"lhs":6598,"rhs":6596},"4 - 3*2",{"lhs":6600,"rhs":2193},"-2 - (-2)",{"lhs":6602,"rhs":3154},"-2 \u002F (-2)",{"lhs":6604,"rhs":3154},"3 - 2",{"lhs":6606,"rhs":6607},"5 - 3*2","-1",{"lhs":6609,"rhs":3154},"-1 - (-2)",{"lhs":6611,"rhs":6596},"det([[1, 1], [1, -1]])",{"lhs":6613,"rhs":5157,"where":6614},"x + y",{"x":6615,"y":6582},3,{"lhs":6617,"rhs":3154,"where":6618},"x - y",{"x":6615,"y":6582},"A \\in \\mathbb{R}^{m \\times n},\\ \\vec b \\in \\mathbb{R}^{m}","\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>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{m \\times n},\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:0.7224em;vertical-align:-0.0391em;\">\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:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\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 mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec b \\in \\mathbb{R}^{m}\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:1.0165em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"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\"\u002F>\u003C\u002Fsvg>\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\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 mathnormal mtight\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","linear-system-solvability","A\\vec x = \\vec b \\text{ lösbar} \\iff \\operatorname{rg}(A) = \\operatorname{rg}(A \\mid \\vec b)","\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>A\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmrow>\u003Cmtext> l\u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmtext>o\u003C\u002Fmtext>\u003Cmo>¨\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>sbar\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">rg\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">rg\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∣\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\\vec x = \\vec b \\text{ lösbar} \\iff \\operatorname{rg}(A) = \\operatorname{rg}(A \\mid \\vec b)\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:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"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\"\u002F>\u003C\u002Fsvg>\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:1.0014em;vertical-align:-0.024em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"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\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> l\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">o\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.25em;\">\u003Cspan class=\"mord\">¨\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">sbar\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\" style=\"margin-right:0.0139em;\">rg\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan 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