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(C_{ij})",[574,1159,1161,1180],{"className":1160,"ariaHidden":620},[619],[574,1162,1164,1168,1171,1174,1177],{"className":1163},[624],[574,1165],{"className":1166,"style":1167},[628],"height:0.6833em;",[574,1169,739],{"className":1170,"style":806},[637,646],[574,1172],{"className":1173,"style":864},[709],[574,1175,748],{"className":1176},[868],[574,1178],{"className":1179,"style":864},[709],[574,1181,1183,1187,1190,1233],{"className":1182},[624],[574,1184],{"className":1185,"style":1186},[628],"height:1.0361em;vertical-align:-0.2861em;",[574,1188,604],{"className":1189},[642],[574,1191,1193,1196],{"className":1192},[637],[574,1194,739],{"className":1195,"style":806},[637,646],[574,1197,1199],{"className":1198},[810],[574,1200,1202,1225],{"className":1201},[814,815],[574,1203,1205,1222],{"className":1204},[819],[574,1206,1208],{"className":1207,"style":824},[823],[574,1209,1210,1213],{"style":827},[574,1211],{"className":1212,"style":832},[831],[574,1214,1216],{"className":1215},[836,837,838,839],[574,1217,1219],{"className":1218},[637,839],[574,1220,846],{"className":1221,"style":714},[637,646,839],[574,1223,851],{"className":1224},[850],[574,1226,1228],{"className":1227},[819],[574,1229,1231],{"className":1230,"style":858},[823],[574,1232],{},[574,1234,610],{"className":1235},[650]," transponieren: ",[574,1238,1240,1271],{"className":1239},[577],[574,1241,1243],{"className":1242},[581],[583,1244,1245],{"xmlns":585},[587,1246,1247,1268],{},[590,1248,1249,1251,1253,1255,1257,1259,1261],{},[593,1250,596],{"mathvariant":595},[598,1252,600],{},[598,1254,604],{"stretchy":603},[593,1256,607],{},[598,1258,610],{"stretchy":603},[598,1260,748],{},[759,1262,1263,1265],{},[593,1264,739],{},[593,1266,1267],{},"T",[612,1269,1270],{"encoding":614},"\\operatorname{adj}(A) = C^T",[574,1272,1274,1304],{"className":1273,"ariaHidden":620},[619],[574,1275,1277,1280,1286,1289,1292,1295,1298,1301],{"className":1276},[624],[574,1278],{"className":1279,"style":629},[628],[574,1281,1283],{"className":1282},[633],[574,1284,596],{"className":1285},[637,638],[574,1287,604],{"className":1288},[642],[574,1290,607],{"className":1291},[637,646],[574,1293,610],{"className":1294},[650],[574,1296],{"className":1297,"style":864},[709],[574,1299,748],{"className":1300},[868],[574,1302],{"className":1303,"style":864},[709],[574,1305,1307,1311],{"className":1306},[624],[574,1308],{"className":1309,"style":1310},[628],"height:0.8413em;",[574,1312,1314,1317],{"className":1313},[637],[574,1315,739],{"className":1316,"style":806},[637,646],[574,1318,1320],{"className":1319},[810],[574,1321,1323],{"className":1322},[814],[574,1324,1326],{"className":1325},[819],[574,1327,1329],{"className":1328,"style":1310},[823],[574,1330,1331,1334],{"style":909},[574,1332],{"className":1333,"style":832},[831],[574,1335,1337],{"className":1336},[836,837,838,839],[574,1338,1267],{"className":1339,"style":1340},[637,646,839],"margin-right:0.1389em;",[565,1342,1343,1344,1538,1539,1644,1645,1715,1716,1770],{},"Es gilt ",[574,1345,1347,1403],{"className":1346},[577],[574,1348,1350],{"className":1349},[581],[583,1351,1352],{"xmlns":585},[587,1353,1354,1400],{},[590,1355,1356,1358,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397],{},[593,1357,607],{},[598,1359,1360],{},"⋅",[593,1362,596],{"mathvariant":595},[598,1364,600],{},[598,1366,604],{"stretchy":603},[593,1368,607],{},[598,1370,610],{"stretchy":603},[598,1372,748],{},[593,1374,596],{"mathvariant":595},[598,1376,600],{},[598,1378,604],{"stretchy":603},[593,1380,607],{},[598,1382,610],{"stretchy":603},[598,1384,1360],{},[593,1386,607],{},[598,1388,748],{},[593,1390,774],{},[598,1392,600],{},[593,1394,607],{},[598,1396,1360],{},[593,1398,1399],{},"E",[612,1401,1402],{"encoding":614},"A \\cdot \\operatorname{adj}(A) = \\operatorname{adj}(A) \\cdot A = \\det A \\cdot E",[574,1404,1406,1425,1455,1485,1503,1528],{"className":1405,"ariaHidden":620},[619],[574,1407,1409,1412,1415,1419,1422],{"className":1408},[624],[574,1410],{"className":1411,"style":1167},[628],[574,1413,607],{"className":1414},[637,646],[574,1416],{"className":1417,"style":1418},[709],"margin-right:0.2222em;",[574,1420,1360],{"className":1421},[925],[574,1423],{"className":1424,"style":1418},[709],[574,1426,1428,1431,1437,1440,1443,1446,1449,1452],{"className":1427},[624],[574,1429],{"className":1430,"style":629},[628],[574,1432,1434],{"className":1433},[633],[574,1435,596],{"className":1436},[637,638],[574,1438,604],{"className":1439},[642],[574,1441,607],{"className":1442},[637,646],[574,1444,610],{"className":1445},[650],[574,1447],{"className":1448,"style":864},[709],[574,1450,748],{"className":1451},[868],[574,1453],{"className":1454,"style":864},[709],[574,1456,1458,1461,1467,1470,1473,1476,1479,1482],{"className":1457},[624],[574,1459],{"className":1460,"style":629},[628],[574,1462,1464],{"className":1463},[633],[574,1465,596],{"className":1466},[637,638],[574,1468,604],{"className":1469},[642],[574,1471,607],{"className":1472},[637,646],[574,1474,610],{"className":1475},[650],[574,1477],{"className":1478,"style":1418},[709],[574,1480,1360],{"className":1481},[925],[574,1483],{"className":1484,"style":1418},[709],[574,1486,1488,1491,1494,1497,1500],{"className":1487},[624],[574,1489],{"className":1490,"style":1167},[628],[574,1492,607],{"className":1493},[637,646],[574,1495],{"className":1496,"style":864},[709],[574,1498,748],{"className":1499},[868],[574,1501],{"className":1502,"style":864},[709],[574,1504,1506,1510,1513,1516,1519,1522,1525],{"className":1505},[624],[574,1507],{"className":1508,"style":1509},[628],"height:0.6944em;",[574,1511,774],{"className":1512},[633],[574,1514],{"className":1515,"style":710},[709],[574,1517,607],{"className":1518},[637,646],[574,1520],{"className":1521,"style":1418},[709],[574,1523,1360],{"className":1524},[925],[574,1526],{"className":1527,"style":1418},[709],[574,1529,1531,1534],{"className":1530},[624],[574,1532],{"className":1533,"style":1167},[628],[574,1535,1399],{"className":1536,"style":1537},[637,646],"margin-right:0.0576em;",". Ist ",[574,1540,1542,1566],{"className":1541},[577],[574,1543,1545],{"className":1544},[581],[583,1546,1547],{"xmlns":585},[587,1548,1549,1563],{},[590,1550,1551,1553,1555,1557,1560],{},[593,1552,774],{},[598,1554,600],{},[593,1556,607],{},[598,1558,1559],{"mathvariant":595},"≠",[755,1561,1562],{},"0",[612,1564,1565],{"encoding":614},"\\det A \\neq 0",[574,1567,1569,1634],{"className":1568,"ariaHidden":620},[619],[574,1570,1572,1576,1579,1582,1585,1588,1631],{"className":1571},[624],[574,1573],{"className":1574,"style":1575},[628],"height:0.8889em;vertical-align:-0.1944em;",[574,1577,774],{"className":1578},[633],[574,1580],{"className":1581,"style":710},[709],[574,1583,607],{"className":1584},[637,646],[574,1586],{"className":1587,"style":864},[709],[574,1589,1591,1624,1628],{"className":1590},[868],[574,1592,1594],{"className":1593},[868],[574,1595,1598],{"className":1596},[637,1597],"vbox",[574,1599,1602],{"className":1600},[1601],"thinbox",[574,1603,1606,1609,1620],{"className":1604},[1605],"rlap",[574,1607],{"className":1608,"style":1575},[628],[574,1610,1613],{"className":1611},[1612],"inner",[574,1614,1616],{"className":1615},[637],[574,1617,1619],{"className":1618},[868],"",[574,1621],{"className":1622},[1623],"fix",[574,1625],{"className":1626},[709,1627],"nobreak",[574,1629,748],{"className":1630},[868],[574,1632],{"className":1633,"style":864},[709],[574,1635,1637,1641],{"className":1636},[624],[574,1638],{"className":1639,"style":1640},[628],"height:0.6444em;",[574,1642,1562],{"className":1643},[637],", folgt daraus die Formel für ",[574,1646,1648,1670],{"className":1647},[577],[574,1649,1651],{"className":1650},[581],[583,1652,1653],{"xmlns":585},[587,1654,1655,1667],{},[590,1656,1657],{},[759,1658,1659,1661],{},[593,1660,607],{},[590,1662,1663,1665],{},[598,1664,753],{},[755,1666,757],{},[612,1668,1669],{"encoding":614},"A^{-1}",[574,1671,1673],{"className":1672,"ariaHidden":620},[619],[574,1674,1676,1680],{"className":1675},[624],[574,1677],{"className":1678,"style":1679},[628],"height:0.8141em;",[574,1681,1683,1686],{"className":1682},[637],[574,1684,607],{"className":1685},[637,646],[574,1687,1689],{"className":1688},[810],[574,1690,1692],{"className":1691},[814],[574,1693,1695],{"className":1694},[819],[574,1696,1698],{"className":1697,"style":1679},[823],[574,1699,1700,1703],{"style":909},[574,1701],{"className":1702,"style":832},[831],[574,1704,1706],{"className":1705},[836,837,838,839],[574,1707,1709,1712],{"className":1708},[637,839],[574,1710,753],{"className":1711},[637,839],[574,1713,757],{"className":1714},[637,839],". Für ",[574,1717,1719,1739],{"className":1718},[577],[574,1720,1722],{"className":1721},[581],[583,1723,1724],{"xmlns":585},[587,1725,1726,1736],{},[590,1727,1728,1731,1734],{},[755,1729,1730],{},"2",[598,1732,1733],{},"×",[755,1735,1730],{},[612,1737,1738],{"encoding":614},"2 \\times 2",[574,1740,1742,1761],{"className":1741,"ariaHidden":620},[619],[574,1743,1745,1749,1752,1755,1758],{"className":1744},[624],[574,1746],{"className":1747,"style":1748},[628],"height:0.7278em;vertical-align:-0.0833em;",[574,1750,1730],{"className":1751},[637],[574,1753],{"className":1754,"style":1418},[709],[574,1756,1733],{"className":1757},[925],[574,1759],{"className":1760,"style":1418},[709],[574,1762,1764,1767],{"className":1763},[624],[574,1765],{"className":1766,"style":1640},[628],[574,1768,1730],{"className":1769},[637],"-Matrizen ergibt sich die bekannte Regel „Diagonale tauschen, Nebendiagonale negieren\".",[565,1772,1773,1774,1826,1827,1895,1896,1924],{},"Für ",[574,1775,1777,1796],{"className":1776},[577],[574,1778,1780],{"className":1779},[581],[583,1781,1782],{"xmlns":585},[587,1783,1784,1793],{},[590,1785,1786,1789,1791],{},[755,1787,1788],{},"3",[598,1790,1733],{},[755,1792,1788],{},[612,1794,1795],{"encoding":614},"3 \\times 3",[574,1797,1799,1817],{"className":1798,"ariaHidden":620},[619],[574,1800,1802,1805,1808,1811,1814],{"className":1801},[624],[574,1803],{"className":1804,"style":1748},[628],[574,1806,1788],{"className":1807},[637],[574,1809],{"className":1810,"style":1418},[709],[574,1812,1733],{"className":1813},[925],[574,1815],{"className":1816,"style":1418},[709],[574,1818,1820,1823],{"className":1819},[624],[574,1821],{"className":1822,"style":1640},[628],[574,1824,1788],{"className":1825},[637],"-Matrizen ist das Verfahren handlich, für größere Matrizen ist der Gauß-Jordan-Algorithmus schneller. Die Formel ist trotzdem theoretisch wichtig: Sie zeigt, dass die Einträge von ",[574,1828,1830,1851],{"className":1829},[577],[574,1831,1833],{"className":1832},[581],[583,1834,1835],{"xmlns":585},[587,1836,1837,1849],{},[590,1838,1839],{},[759,1840,1841,1843],{},[593,1842,607],{},[590,1844,1845,1847],{},[598,1846,753],{},[755,1848,757],{},[612,1850,1669],{"encoding":614},[574,1852,1854],{"className":1853,"ariaHidden":620},[619],[574,1855,1857,1860],{"className":1856},[624],[574,1858],{"className":1859,"style":1679},[628],[574,1861,1863,1866],{"className":1862},[637],[574,1864,607],{"className":1865},[637,646],[574,1867,1869],{"className":1868},[810],[574,1870,1872],{"className":1871},[814],[574,1873,1875],{"className":1874},[819],[574,1876,1878],{"className":1877,"style":1679},[823],[574,1879,1880,1883],{"style":909},[574,1881],{"className":1882,"style":832},[831],[574,1884,1886],{"className":1885},[836,837,838,839],[574,1887,1889,1892],{"className":1888},[637,839],[574,1890,753],{"className":1891},[637,839],[574,1893,757],{"className":1894},[637,839]," rationale Funktionen der Einträge von ",[574,1897,1899,1912],{"className":1898},[577],[574,1900,1902],{"className":1901},[581],[583,1903,1904],{"xmlns":585},[587,1905,1906,1910],{},[590,1907,1908],{},[593,1909,607],{},[612,1911,607],{"encoding":614},[574,1913,1915],{"className":1914,"ariaHidden":620},[619],[574,1916,1918,1921],{"className":1917},[624],[574,1919],{"className":1920,"style":1167},[628],[574,1922,607],{"className":1923},[637,646]," sind, und sie steckt hinter der Cramerschen Regel.",[560,1926,1928],{"id":1927},"beispiele","Beispiele",[574,1930,1933],{"className":1931},[1932],"katex-display",[574,1934,1936,2044],{"className":1935},[577],[574,1937,1939],{"className":1938},[581],[583,1940,1942],{"xmlns":585,"display":1941},"block",[587,1943,1944,2041],{},[590,1945,1946,1948,1950,2025,2027,2030,2032,2034,2036,2038],{},[593,1947,607],{},[598,1949,748],{},[590,1951,1952,1954,2023],{},[598,1953,604],{"fence":620},[1955,1956,1960,1983,2003],"mtable",{"rowspacing":1957,"columnalign":1958,"columnspacing":1959},"0.16em","center center center","1em",[1961,1962,1963,1971,1977],"mtr",{},[1964,1965,1966],"mtd",{},[1967,1968,1969],"mstyle",{"scriptlevel":1562,"displaystyle":603},[755,1970,757],{},[1964,1972,1973],{},[1967,1974,1975],{"scriptlevel":1562,"displaystyle":603},[755,1976,1562],{},[1964,1978,1979],{},[1967,1980,1981],{"scriptlevel":1562,"displaystyle":603},[755,1982,1730],{},[1961,1984,1985,1991,1997],{},[1964,1986,1987],{},[1967,1988,1989],{"scriptlevel":1562,"displaystyle":603},[755,1990,1730],{},[1964,1992,1993],{},[1967,1994,1995],{"scriptlevel":1562,"displaystyle":603},[755,1996,757],{},[1964,1998,1999],{},[1967,2000,2001],{"scriptlevel":1562,"displaystyle":603},[755,2002,1562],{},[1961,2004,2005,2011,2017],{},[1964,2006,2007],{},[1967,2008,2009],{"scriptlevel":1562,"displaystyle":603},[755,2010,1562],{},[1964,2012,2013],{},[1967,2014,2015],{"scriptlevel":1562,"displaystyle":603},[755,2016,757],{},[1964,2018,2019],{},[1967,2020,2021],{"scriptlevel":1562,"displaystyle":603},[755,2022,757],{},[598,2024,610],{"fence":620},[598,2026,678],{"separator":620},[709,2028],{"width":2029},"2em",[593,2031,774],{},[598,2033,600],{},[593,2035,607],{},[598,2037,748],{},[755,2039,2040],{},"5",[612,2042,2043],{"encoding":614},"A = \\begin{pmatrix} 1 & 0 & 2 \\\\ 2 & 1 & 0 \\\\ 0 & 1 & 1 \\end{pmatrix}, \\qquad \\det A = 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= \\frac{1}{5} \\begin{pmatrix} 1 & 2 & -2 \\\\ -2 & 1 & 4 \\\\ 2 & -1 & 1 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:3963},[814,815],[574,3965,3967,4006],{"className":3966},[819],[574,3968,3970,3984,3995],{"className":3969,"style":2093},[823],[574,3971,3972,3975],{"style":2148},[574,3973],{"className":3974,"style":2152},[831],[574,3976,3978,3981],{"className":3977},[637],[574,3979,753],{"className":3980},[637],[574,3982,1730],{"className":3983},[637],[574,3985,3986,3989],{"style":2161},[574,3987],{"className":3988,"style":2152},[831],[574,3990,3992],{"className":3991},[637],[574,3993,2492],{"className":3994},[637],[574,3996,3997,4000],{"style":2173},[574,3998],{"className":3999,"style":2152},[831],[574,4001,4003],{"className":4002},[637],[574,4004,757],{"className":4005},[637],[574,4007,851],{"className":4008},[850],[574,4010,4012],{"className":4011},[819],[574,4013,4015],{"className":4014,"style":2124},[823],[574,4016],{},[574,4018,4020],{"className":4019},[650],[574,4021,4023],{"className":4022},[2082,2083],[574,4024,4026,4046],{"className":4025},[814,815],[574,4027,4029,4043],{"className":4028},[819],[574,4030,4032],{"className":4031,"style":2093},[823],[574,4033,4034,4037],{"style":2096},[574,4035],{"className":4036,"style":2100},[831],[574,4038,4039],{"style":2103},[2105,4040,4041],{"xmlns":2107,"width":2108,"height":2109,"viewBox":2110},[2112,4042],{"d":2346},[574,4044,851],{"className":4045},[850],[574,4047,4049],{"className":4048},[819],[574,4050,4052],{"className":4051,"style":2124},[823],[574,4053],{},[565,4055,4056,4057,4109,4110,4181,4182,1120],{},"Probe für den Eintrag ",[574,4058,4060,4082],{"className":4059},[577],[574,4061,4063],{"className":4062},[581],[583,4064,4065],{"xmlns":585},[587,4066,4067,4079],{},[590,4068,4069,4071,4073,4075,4077],{},[598,4070,604],{"stretchy":603},[755,4072,757],{},[598,4074,678],{"separator":620},[755,4076,757],{},[598,4078,610],{"stretchy":603},[612,4080,4081],{"encoding":614},"(1, 1)",[574,4083,4085],{"className":4084,"ariaHidden":620},[619],[574,4086,4088,4091,4094,4097,4100,4103,4106],{"className":4087},[624],[574,4089],{"className":4090,"style":629},[628],[574,4092,604],{"className":4093},[642],[574,4095,757],{"className":4096},[637],[574,4098,678],{"className":4099},[705],[574,4101],{"className":4102,"style":710},[709],[574,4104,757],{"className":4105},[637],[574,4107,610],{"className":4108},[650]," von ",[574,4111,4113,4139],{"className":4112},[577],[574,4114,4116],{"className":4115},[581],[583,4117,4118],{"xmlns":585},[587,4119,4120,4136],{},[590,4121,4122,4124,4126,4128,4130,4132,4134],{},[593,4123,607],{},[598,4125,1360],{},[593,4127,596],{"mathvariant":595},[598,4129,600],{},[598,4131,604],{"stretchy":603},[593,4133,607],{},[598,4135,610],{"stretchy":603},[612,4137,4138],{"encoding":614},"A \\cdot \\operatorname{adj}(A)",[574,4140,4142,4160],{"className":4141,"ariaHidden":620},[619],[574,4143,4145,4148,4151,4154,4157],{"className":4144},[624],[574,4146],{"className":4147,"style":1167},[628],[574,4149,607],{"className":4150},[637,646],[574,4152],{"className":4153,"style":1418},[709],[574,4155,1360],{"className":4156},[925],[574,4158],{"className":4159,"style":1418},[709],[574,4161,4163,4166,4172,4175,4178],{"className":4162},[624],[574,4164],{"className":4165,"style":629},[628],[574,4167,4169],{"className":4168},[633],[574,4170,596],{"className":4171},[637,638],[574,4173,604],{"className":4174},[642],[574,4176,607],{"className":4177},[637,646],[574,4179,610],{"className":4180},[650],": ",[574,4183,4185,4237],{"className":4184},[577],[574,4186,4188],{"className":4187},[581],[583,4189,4190],{"xmlns":585},[587,4191,4192,4234],{},[590,4193,4194,4196,4198,4200,4202,4204,4206,4208,4210,4212,4214,4216,4218,4220,4222,4224,4226,4228,4230,4232],{},[755,4195,757],{},[598,4197,1360],{},[755,4199,757],{},[598,4201,769],{},[755,4203,1562],{},[598,4205,1360],{},[598,4207,604],{"stretchy":603},[598,4209,753],{},[755,4211,1730],{},[598,4213,610],{"stretchy":603},[598,4215,769],{},[755,4217,1730],{},[598,4219,1360],{},[755,4221,1730],{},[598,4223,748],{},[755,4225,2040],{},[598,4227,748],{},[593,4229,774],{},[598,4231,600],{},[593,4233,607],{},[612,4235,4236],{"encoding":614},"1 \\cdot 1 + 0 \\cdot (-2) + 2 \\cdot 2 = 5 = \\det A",[574,4238,4240,4258,4276,4294,4321,4339,4357,4375],{"className":4239,"ariaHidden":620},[619],[574,4241,4243,4246,4249,4252,4255],{"className":4242},[624],[574,4244],{"className":4245,"style":1640},[628],[574,4247,757],{"className":4248},[637],[574,4250],{"className":4251,"style":1418},[709],[574,4253,1360],{"className":4254},[925],[574,4256],{"className":4257,"style":1418},[709],[574,4259,4261,4264,4267,4270,4273],{"className":4260},[624],[574,4262],{"className":4263,"style":1748},[628],[574,4265,757],{"className":4266},[637],[574,4268],{"className":4269,"style":1418},[709],[574,4271,769],{"className":4272},[925],[574,4274],{"className":4275,"style":1418},[709],[574,4277,4279,4282,4285,4288,4291],{"className":4278},[624],[574,4280],{"className":4281,"style":1640},[628],[574,4283,1562],{"className":4284},[637],[574,4286],{"className":4287,"style":1418},[709],[574,4289,1360],{"className":4290},[925],[574,4292],{"className":4293,"style":1418},[709],[574,4295,4297,4300,4303,4306,4309,4312,4315,4318],{"className":4296},[624],[574,4298],{"className":4299,"style":629},[628],[574,4301,604],{"className":4302},[642],[574,4304,753],{"className":4305},[637],[574,4307,1730],{"className":4308},[637],[574,4310,610],{"className":4311},[650],[574,4313],{"className":4314,"style":1418},[709],[574,4316,769],{"className":4317},[925],[574,4319],{"className":4320,"style":1418},[709],[574,4322,4324,4327,4330,4333,4336],{"className":4323},[624],[574,4325],{"className":4326,"style":1640},[628],[574,4328,1730],{"className":4329},[637],[574,4331],{"className":4332,"style":1418},[709],[574,4334,1360],{"className":4335},[925],[574,4337],{"className":4338,"style":1418},[709],[574,4340,4342,4345,4348,4351,4354],{"className":4341},[624],[574,4343],{"className":4344,"style":1640},[628],[574,4346,1730],{"className":4347},[637],[574,4349],{"className":4350,"style":864},[709],[574,4352,748],{"className":4353},[868],[574,4355],{"className":4356,"style":864},[709],[574,4358,4360,4363,4366,4369,4372],{"className":4359},[624],[574,4361],{"className":4362,"style":1640},[628],[574,4364,2040],{"className":4365},[637],[574,4367],{"className":4368,"style":864},[709],[574,4370,748],{"className":4371},[868],[574,4373],{"className":4374,"style":864},[709],[574,4376,4378,4381,4384,4387],{"className":4377},[624],[574,4379],{"className":4380,"style":1509},[628],[574,4382,774],{"className":4383},[633],[574,4385],{"className":4386,"style":710},[709],[574,4388,607],{"className":4389},[637,646],[560,4391,4393],{"id":4392},"typische-fehler","Typische Fehler",[4395,4396,4397,4489,4583,4626],"ul",{},[656,4398,4399,4400,4428,4429,4488],{},"Das Transponieren vergessen und die Kofaktormatrix ",[574,4401,4403,4416],{"className":4402},[577],[574,4404,4406],{"className":4405},[581],[583,4407,4408],{"xmlns":585},[587,4409,4410,4414],{},[590,4411,4412],{},[593,4413,739],{},[612,4415,739],{"encoding":614},[574,4417,4419],{"className":4418,"ariaHidden":620},[619],[574,4420,4422,4425],{"className":4421},[624],[574,4423],{"className":4424,"style":1167},[628],[574,4426,739],{"className":4427,"style":806},[637,646]," statt ",[574,4430,4432,4450],{"className":4431},[577],[574,4433,4435],{"className":4434},[581],[583,4436,4437],{"xmlns":585},[587,4438,4439,4447],{},[590,4440,4441],{},[759,4442,4443,4445],{},[593,4444,739],{},[593,4446,1267],{},[612,4448,4449],{"encoding":614},"C^T",[574,4451,4453],{"className":4452,"ariaHidden":620},[619],[574,4454,4456,4459],{"className":4455},[624],[574,4457],{"className":4458,"style":1310},[628],[574,4460,4462,4465],{"className":4461},[637],[574,4463,739],{"className":4464,"style":806},[637,646],[574,4466,4468],{"className":4467},[810],[574,4469,4471],{"className":4470},[814],[574,4472,4474],{"className":4473},[819],[574,4475,4477],{"className":4476,"style":1310},[823],[574,4478,4479,4482],{"style":909},[574,4480],{"className":4481,"style":832},[831],[574,4483,4485],{"className":4484},[836,837,838,839],[574,4486,1267],{"className":4487,"style":1340},[637,646,839]," verwenden. Bei symmetrischen Matrizen fällt das nicht auf, sonst schon.",[656,4490,4491,4492,4582],{},"Das Schachbrettvorzeichen ",[574,4493,4495,4525],{"className":4494},[577],[574,4496,4498],{"className":4497},[581],[583,4499,4500],{"xmlns":585},[587,4501,4502,4522],{},[590,4503,4504,4506,4508,4510],{},[598,4505,604],{"stretchy":603},[598,4507,753],{},[755,4509,757],{},[759,4511,4512,4514],{},[598,4513,610],{"stretchy":603},[590,4515,4516,4518,4520],{},[593,4517,675],{},[598,4519,769],{},[593,4521,681],{},[612,4523,4524],{"encoding":614},"(-1)^{i+j}",[574,4526,4528],{"className":4527,"ariaHidden":620},[619],[574,4529,4531,4535,4538,4541,4544],{"className":4530},[624],[574,4532],{"className":4533,"style":4534},[628],"height:1.0747em;vertical-align:-0.25em;",[574,4536,604],{"className":4537},[642],[574,4539,753],{"className":4540},[637],[574,4542,757],{"className":4543},[637],[574,4545,4547,4550],{"className":4546},[650],[574,4548,610],{"className":4549},[650],[574,4551,4553],{"className":4552},[810],[574,4554,4556],{"className":4555},[814],[574,4557,4559],{"className":4558},[819],[574,4560,4562],{"className":4561,"style":906},[823],[574,4563,4564,4567],{"style":909},[574,4565],{"className":4566,"style":832},[831],[574,4568,4570],{"className":4569},[836,837,838,839],[574,4571,4573,4576,4579],{"className":4572},[637,839],[574,4574,675],{"className":4575},[637,646,839],[574,4577,769],{"className":4578},[925,839],[574,4580,681],{"className":4581,"style":714},[637,646,839]," weglassen.",[656,4584,4585,4586,4625],{},"Am Ende nicht durch ",[574,4587,4589,4607],{"className":4588},[577],[574,4590,4592],{"className":4591},[581],[583,4593,4594],{"xmlns":585},[587,4595,4596,4604],{},[590,4597,4598,4600,4602],{},[593,4599,774],{},[598,4601,600],{},[593,4603,607],{},[612,4605,4606],{"encoding":614},"\\det A",[574,4608,4610],{"className":4609,"ariaHidden":620},[619],[574,4611,4613,4616,4619,4622],{"className":4612},[624],[574,4614],{"className":4615,"style":1509},[628],[574,4617,774],{"className":4618},[633],[574,4620],{"className":4621,"style":710},[709],[574,4623,607],{"className":4624},[637,646]," teilen.",[656,4627,4628,4629,4690,4691,4784],{},"Die Formel anwenden, obwohl ",[574,4630,4632,4654],{"className":4631},[577],[574,4633,4635],{"className":4634},[581],[583,4636,4637],{"xmlns":585},[587,4638,4639,4651],{},[590,4640,4641,4643,4645,4647,4649],{},[593,4642,774],{},[598,4644,600],{},[593,4646,607],{},[598,4648,748],{},[755,4650,1562],{},[612,4652,4653],{"encoding":614},"\\det A = 0",[574,4655,4657,4681],{"className":4656,"ariaHidden":620},[619],[574,4658,4660,4663,4666,4669,4672,4675,4678],{"className":4659},[624],[574,4661],{"className":4662,"style":1509},[628],[574,4664,774],{"className":4665},[633],[574,4667],{"className":4668,"style":710},[709],[574,4670,607],{"className":4671},[637,646],[574,4673],{"className":4674,"style":864},[709],[574,4676,748],{"className":4677},[868],[574,4679],{"className":4680,"style":864},[709],[574,4682,4684,4687],{"className":4683},[624],[574,4685],{"className":4686,"style":1640},[628],[574,4688,1562],{"className":4689},[637]," ist. Dann existiert keine Inverse; ",[574,4692,4694,4724],{"className":4693},[577],[574,4695,4697],{"className":4696},[581],[583,4698,4699],{"xmlns":585},[587,4700,4701,4721],{},[590,4702,4703,4705,4707,4709,4711,4713,4715,4717,4719],{},[593,4704,607],{},[598,4706,1360],{},[593,4708,596],{"mathvariant":595},[598,4710,600],{},[598,4712,604],{"stretchy":603},[593,4714,607],{},[598,4716,610],{"stretchy":603},[598,4718,748],{},[755,4720,1562],{},[612,4722,4723],{"encoding":614},"A \\cdot \\operatorname{adj}(A) = 0",[574,4725,4727,4745,4775],{"className":4726,"ariaHidden":620},[619],[574,4728,4730,4733,4736,4739,4742],{"className":4729},[624],[574,4731],{"className":4732,"style":1167},[628],[574,4734,607],{"className":4735},[637,646],[574,4737],{"className":4738,"style":1418},[709],[574,4740,1360],{"className":4741},[925],[574,4743],{"className":4744,"style":1418},[709],[574,4746,4748,4751,4757,4760,4763,4766,4769,4772],{"className":4747},[624],[574,4749],{"className":4750,"style":629},[628],[574,4752,4754],{"className":4753},[633],[574,4755,596],{"className":4756},[637,638],[574,4758,604],{"className":4759},[642],[574,4761,607],{"className":4762},[637,646],[574,4764,610],{"className":4765},[650],[574,4767],{"className":4768,"style":864},[709],[574,4770,748],{"className":4771},[868],[574,4773],{"className":4774,"style":864},[709],[574,4776,4778,4781],{"className":4777},[624],[574,4779],{"className":4780,"style":1640},[628],[574,4782,1562],{"className":4783},[637]," bleibt aber richtig.",{"title":4786,"searchDepth":4787,"depth":4787,"links":4788},"",2,[4789,4790,4791],{"id":562,"depth":4787,"text":563},{"id":1927,"depth":4787,"text":1928},{"id":4392,"depth":4787,"text":4393},[4793,4796,4799,4801,4803,4806,4808,4810,4812,4815,4817,4819,4821,4824,4827,4830,4832,4834,4837,4839,4842,4844],{"lhs":4794,"rhs":4795},"inv([[a + 3, b], [c, d + 3]])[1, 2] * det([[a + 3, b], [c, d + 3]])","-b",{"lhs":4797,"rhs":4798},"inv([[a + 3, b], [c, d + 3]])[2, 1] * det([[a + 3, b], [c, d + 3]])","-c",{"lhs":4800,"rhs":2040},"det([[1, 0, 2], [2, 1, 0], [0, 1, 1]])",{"lhs":4802,"rhs":757},"1*1 - 0*1",{"lhs":4804,"rhs":4805},"-(2*1 - 0*0)","-2",{"lhs":4807,"rhs":1730},"2*1 - 1*0",{"lhs":4809,"rhs":1730},"-(0*1 - 2*1)",{"lhs":4811,"rhs":757},"1*1 - 2*0",{"lhs":4813,"rhs":4814},"-(1*1 - 0*0)","-1",{"lhs":4816,"rhs":4805},"0*0 - 2*1",{"lhs":4818,"rhs":2492},"-(1*0 - 2*2)",{"lhs":4820,"rhs":757},"1*1 - 0*2",{"lhs":4822,"rhs":4823},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[1, 1]","1\u002F5",{"lhs":4825,"rhs":4826},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[1, 2]","2\u002F5",{"lhs":4828,"rhs":4829},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[1, 3]","-2\u002F5",{"lhs":4831,"rhs":4829},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[2, 1]",{"lhs":4833,"rhs":4823},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[2, 2]",{"lhs":4835,"rhs":4836},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[2, 3]","4\u002F5",{"lhs":4838,"rhs":4826},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[3, 1]",{"lhs":4840,"rhs":4841},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[3, 2]","-1\u002F5",{"lhs":4843,"rhs":4823},"inv([[1, 0, 2], [2, 1, 0], [0, 1, 1]])[3, 3]",{"lhs":4845,"rhs":2040},"1*1 + 0*(-2) + 2*2","A \\in \\mathbb{R}^{n \\times n},\\ \\det A \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\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}^{n \\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\">n\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>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\det A \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","adjugate-inverse","A^{-1} = \\frac{1}{\\det A} \\operatorname{adj}(A), \\qquad \\operatorname{adj}(A)_{ij} = (-1)^{i+j} \\det A_{ji}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmi mathvariant=\"normal\">adj\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi mathvariant=\"normal\">adj\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{-1} = \\frac{1}{\\det A} \\operatorname{adj}(A), \\qquad \\operatorname{adj}(A)_{ij} = (-1)^{i+j} \\det A_{ji}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">adj\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">adj\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\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:0.2861em;\">\u003Cspan>\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:1.1608em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8747em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-ueber-adjunkte",[],[4859,4860,4861,4862],"inverse-2x2","laplace-expansion","cramers-rule","inverse-rules",{"title":548,"description":4786},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-ueber-adjunkte","Die Inverse ist die Adjunkte, also die transponierte Matrix der Kofaktoren, geteilt durch die Determinante.",[4867,4868,4869,4870,4871],"inverse","adjunkte","kofaktor","determinante","matrix",[4873,4876,4879,4883],{"symbol":607,"meaning":4874,"symbolHtml":4875},"invertierbare n × n-Matrix","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":615,"meaning":4877,"symbolHtml":4878},"Adjunkte von A, die Transponierte der Kofaktormatrix","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">adj\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{adj}(A)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">adj\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4880,"meaning":4881,"symbolHtml":4882},"A_{ji}","Streichungsmatrix ohne Zeile j und Spalte i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A_{ji}\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:0.9694em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4606,"meaning":4884,"symbolHtml":4885},"Determinante von A","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\det A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lMl2kOvFsYYNx2IM_0QK7_xQSiznB3h0530Oj7dUdFo",[4888,4891,4894,4897],{"stem":4889,"title":4890,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fcramersche-regel","Cramersche Regel",{"stem":4892,"title":4893,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-2x2-matrix","Inverse einer 2×2-Matrix",{"stem":4895,"title":4896,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Flaplace-entwicklung","Laplace-Entwicklung",{"stem":4898,"title":4899,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-inverse","Rechenregeln für die Inverse",1793824278408]