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lässt:",[574,1073,1076],{"className":1074},[1075],"katex-display",[574,1077,1079,1172],{"className":1078},[577],[574,1080,1082],{"className":1081},[581],[583,1083,1085],{"xmlns":585,"display":1084},"block",[587,1086,1087,1169],{},[590,1088,1089,1095,1105,1108,1110,1112,1118,1128,1131,1138,1142,1145,1147,1153,1155,1157,1159,1165,1167],{},[593,1090,1091,1093],{},[600,1092,936],{},[608,1094,610],{},[593,1096,1097,1103],{},[596,1098,1099,1101],{"accent":598},[600,1100,602],{},[604,1102,606],{},[608,1104,610],{},[604,1106,1107],{},"+",[604,1109,616],{},[604,1111,1107],{},[593,1113,1114,1116],{},[600,1115,936],{},[600,1117,629],{},[593,1119,1120,1126],{},[596,1121,1122,1124],{"accent":598},[600,1123,602],{},[604,1125,606],{},[600,1127,629],{},[604,1129,1130],{},"=",[596,1132,1133,1136],{"accent":598},[608,1134,1135],{},"0",[604,1137,606],{},[1139,1140,1141],"mtext",{},"  ",[604,1143,1144],{},"⇒",[1139,1146,1141],{},[593,1148,1149,1151],{},[600,1150,936],{},[608,1152,610],{},[604,1154,1130],{},[604,1156,616],{},[604,1158,1130],{},[593,1160,1161,1163],{},[600,1162,936],{},[600,1164,629],{},[604,1166,1130],{},[608,1168,1135],{},[631,1170,1171],{"encoding":633},"r_1 \\vec{a}_1 + \\ldots + r_n \\vec{a}_n = \\vec{0} \\;\\Rightarrow\\; r_1 = \\ldots = r_n = 0",[574,1173,1175,1305,1324,1453,1511,1567,1586,1641],{"className":1174,"ariaHidden":598},[638],[574,1176,1178,1182,1222,1294,1298,1302],{"className":1177},[642],[574,1179],{"className":1180,"style":1181},[646],"height:0.864em;vertical-align:-0.15em;",[574,1183,1185,1188],{"className":1184},[651],[574,1186,936],{"className":1187,"style":970},[651,680],[574,1189,1191],{"className":1190},[712],[574,1192,1194,1214],{"className":1193},[659,716],[574,1195,1197,1211],{"className":1196},[663],[574,1198,1200],{"className":1199,"style":723},[667],[574,1201,1202,1205],{"style":985},[574,1203],{"className":1204,"style":730},[675],[574,1206,1208],{"className":1207},[734,735,736,737],[574,1209,610],{"className":1210},[651,737],[574,1212,745],{"className":1213},[744],[574,1215,1217],{"className":1216},[663],[574,1218,1220],{"className":1219,"style":752},[667],[574,1221],{},[574,1223,1225,1260],{"className":1224},[651],[574,1226,1228],{"className":1227},[651,655],[574,1229,1231],{"className":1230},[659],[574,1232,1234],{"className":1233},[663],[574,1235,1237,1245],{"className":1236,"style":668},[667],[574,1238,1239,1242],{"style":671},[574,1240],{"className":1241,"style":676},[675],[574,1243,602],{"className":1244},[651,680],[574,1246,1247,1250],{"style":671},[574,1248],{"className":1249,"style":676},[675],[574,1251,1253],{"className":1252,"style":690},[689],[574,1254,1256],{"className":1255,"style":695},[694],[697,1257,1258],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,1259],{"d":708},[574,1261,1263],{"className":1262},[712],[574,1264,1266,1286],{"className":1265},[659,716],[574,1267,1269,1283],{"className":1268},[663],[574,1270,1272],{"className":1271,"style":723},[667],[574,1273,1274,1277],{"style":726},[574,1275],{"className":1276,"style":730},[675],[574,1278,1280],{"className":1279},[734,735,736,737],[574,1281,610],{"className":1282},[651,737],[574,1284,745],{"className":1285},[744],[574,1287,1289],{"className":1288},[663],[574,1290,1292],{"className":1291,"style":752},[667],[574,1293],{},[574,1295],{"className":1296,"style":1297},[762],"margin-right:0.2222em;",[574,1299,1107],{"className":1300},[1301],"mbin",[574,1303],{"className":1304,"style":1297},[762],[574,1306,1308,1312,1315,1318,1321],{"className":1307},[642],[574,1309],{"className":1310,"style":1311},[646],"height:0.6667em;vertical-align:-0.0833em;",[574,1313,616],{"className":1314},[767],[574,1316],{"className":1317,"style":1297},[762],[574,1319,1107],{"className":1320},[1301],[574,1322],{"className":1323,"style":1297},[762],[574,1325,1327,1330,1370,1442,1446,1450],{"className":1326},[642],[574,1328],{"className":1329,"style":1181},[646],[574,1331,1333,1336],{"className":1332},[651],[574,1334,936],{"className":1335,"style":970},[651,680],[574,1337,1339],{"className":1338},[712],[574,1340,1342,1362],{"className":1341},[659,716],[574,1343,1345,1359],{"className":1344},[663],[574,1346,1348],{"className":1347,"style":827},[667],[574,1349,1350,1353],{"style":985},[574,1351],{"className":1352,"style":730},[675],[574,1354,1356],{"className":1355},[734,735,736,737],[574,1357,629],{"className":1358},[651,680,737],[574,1360,745],{"className":1361},[744],[574,1363,1365],{"className":1364},[663],[574,1366,1368],{"className":1367,"style":752},[667],[574,1369],{},[574,1371,1373,1408],{"className":1372},[651],[574,1374,1376],{"className":1375},[651,655],[574,1377,1379],{"className":1378},[659],[574,1380,1382],{"className":1381},[663],[574,1383,1385,1393],{"className":1384,"style":668},[667],[574,1386,1387,1390],{"style":671},[574,1388],{"className":1389,"style":676},[675],[574,1391,602],{"className":1392},[651,680],[574,1394,1395,1398],{"style":671},[574,1396],{"className":1397,"style":676},[675],[574,1399,1401],{"className":1400,"style":690},[689],[574,1402,1404],{"className":1403,"style":695},[694],[697,1405,1406],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,1407],{"d":708},[574,1409,1411],{"className":1410},[712],[574,1412,1414,1434],{"className":1413},[659,716],[574,1415,1417,1431],{"className":1416},[663],[574,1418,1420],{"className":1419,"style":827},[667],[574,1421,1422,1425],{"style":726},[574,1423],{"className":1424,"style":730},[675],[574,1426,1428],{"className":1427},[734,735,736,737],[574,1429,629],{"className":1430},[651,680,737],[574,1432,745],{"className":1433},[744],[574,1435,1437],{"className":1436},[663],[574,1438,1440],{"className":1439,"style":752},[667],[574,1441],{},[574,1443],{"className":1444,"style":1445},[762],"margin-right:0.2778em;",[574,1447,1130],{"className":1448},[1449],"mrel",[574,1451],{"className":1452,"style":1445},[762],[574,1454,1456,1460,1496,1499,1502,1505,1508],{"className":1455},[642],[574,1457],{"className":1458,"style":1459},[646],"height:0.9274em;",[574,1461,1463],{"className":1462},[651,655],[574,1464,1466],{"className":1465},[659],[574,1467,1469],{"className":1468},[663],[574,1470,1472,1480],{"className":1471,"style":1459},[667],[574,1473,1474,1477],{"style":671},[574,1475],{"className":1476,"style":676},[675],[574,1478,1135],{"className":1479},[651],[574,1481,1483,1486],{"style":1482},"top:-3.2134em;",[574,1484],{"className":1485,"style":676},[675],[574,1487,1489],{"className":1488,"style":690},[689],[574,1490,1492],{"className":1491,"style":695},[694],[697,1493,1494],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,1495],{"d":708},[574,1497],{"className":1498,"style":1445},[762],[574,1500],{"className":1501,"style":1445},[762],[574,1503,1144],{"className":1504},[1449],[574,1506],{"className":1507,"style":1445},[762],[574,1509],{"className":1510,"style":1445},[762],[574,1512,1514,1518,1558,1561,1564],{"className":1513},[642],[574,1515],{"className":1516,"style":1517},[646],"height:0.5806em;vertical-align:-0.15em;",[574,1519,1521,1524],{"className":1520},[651],[574,1522,936],{"className":1523,"style":970},[651,680],[574,1525,1527],{"className":1526},[712],[574,1528,1530,1550],{"className":1529},[659,716],[574,1531,1533,1547],{"className":1532},[663],[574,1534,1536],{"className":1535,"style":723},[667],[574,1537,1538,1541],{"style":985},[574,1539],{"className":1540,"style":730},[675],[574,1542,1544],{"className":1543},[734,735,736,737],[574,1545,610],{"className":1546},[651,737],[574,1548,745],{"className":1549},[744],[574,1551,1553],{"className":1552},[663],[574,1554,1556],{"className":1555,"style":752},[667],[574,1557],{},[574,1559],{"className":1560,"style":1445},[762],[574,1562,1130],{"className":1563},[1449],[574,1565],{"className":1566,"style":1445},[762],[574,1568,1570,1574,1577,1580,1583],{"className":1569},[642],[574,1571],{"className":1572,"style":1573},[646],"height:0.3669em;",[574,1575,616],{"className":1576},[767],[574,1578],{"className":1579,"style":1445},[762],[574,1581,1130],{"className":1582},[1449],[574,1584],{"className":1585,"style":1445},[762],[574,1587,1589,1592,1632,1635,1638],{"className":1588},[642],[574,1590],{"className":1591,"style":1517},[646],[574,1593,1595,1598],{"className":1594},[651],[574,1596,936],{"className":1597,"style":970},[651,680],[574,1599,1601],{"className":1600},[712],[574,1602,1604,1624],{"className":1603},[659,716],[574,1605,1607,1621],{"className":1606},[663],[574,1608,1610],{"className":1609,"style":827},[667],[574,1611,1612,1615],{"style":985},[574,1613],{"className":1614,"style":730},[675],[574,1616,1618],{"className":1617},[734,735,736,737],[574,1619,629],{"className":1620},[651,680,737],[574,1622,745],{"className":1623},[744],[574,1625,1627],{"className":1626},[663],[574,1628,1630],{"className":1629,"style":752},[667],[574,1631],{},[574,1633],{"className":1634,"style":1445},[762],[574,1636,1130],{"className":1637},[1449],[574,1639],{"className":1640,"style":1445},[762],[574,1642,1644,1648],{"className":1643},[642],[574,1645],{"className":1646,"style":1647},[646],"height:0.6444em;",[574,1649,1135],{"className":1650},[651],[565,1652,1653,1654,1791,1792,1795],{},"Gibt es eine Darstellung mit mindestens einem ",[574,1655,1657,1682],{"className":1656},[577],[574,1658,1660],{"className":1659},[581],[583,1661,1662],{"xmlns":585},[587,1663,1664,1679],{},[590,1665,1666,1673,1677],{},[593,1667,1668,1670],{},[600,1669,936],{},[600,1671,1672],{},"i",[604,1674,1676],{"mathvariant":1675},"normal","≠",[608,1678,1135],{},[631,1680,1681],{"encoding":633},"r_i \\neq 0",[574,1683,1685,1782],{"className":1684,"ariaHidden":598},[638],[574,1686,1688,1692,1733,1736,1779],{"className":1687},[642],[574,1689],{"className":1690,"style":1691},[646],"height:0.8889em;vertical-align:-0.1944em;",[574,1693,1695,1698],{"className":1694},[651],[574,1696,936],{"className":1697,"style":970},[651,680],[574,1699,1701],{"className":1700},[712],[574,1702,1704,1725],{"className":1703},[659,716],[574,1705,1707,1722],{"className":1706},[663],[574,1708,1711],{"className":1709,"style":1710},[667],"height:0.3117em;",[574,1712,1713,1716],{"style":985},[574,1714],{"className":1715,"style":730},[675],[574,1717,1719],{"className":1718},[734,735,736,737],[574,1720,1672],{"className":1721},[651,680,737],[574,1723,745],{"className":1724},[744],[574,1726,1728],{"className":1727},[663],[574,1729,1731],{"className":1730,"style":752},[667],[574,1732],{},[574,1734],{"className":1735,"style":1445},[762],[574,1737,1739,1772,1776],{"className":1738},[1449],[574,1740,1742],{"className":1741},[1449],[574,1743,1746],{"className":1744},[651,1745],"vbox",[574,1747,1750],{"className":1748},[1749],"thinbox",[574,1751,1754,1757,1768],{"className":1752},[1753],"rlap",[574,1755],{"className":1756,"style":1691},[646],[574,1758,1761],{"className":1759},[1760],"inner",[574,1762,1764],{"className":1763},[651],[574,1765,1767],{"className":1766},[1449],"",[574,1769],{"className":1770},[1771],"fix",[574,1773],{"className":1774},[762,1775],"nobreak",[574,1777,1130],{"className":1778},[1449],[574,1780],{"className":1781,"style":1445},[762],[574,1783,1785,1788],{"className":1784},[642],[574,1786],{"className":1787,"style":1647},[646],[574,1789,1135],{"className":1790},[651],", sind sie ",[569,1793,1794],{},"linear abhängig",". Dann ist mindestens einer der Vektoren eine Linearkombination der anderen.",[565,1797,1798],{},"Geometrisch im Raum:",[1800,1801,1802,1810,1846],"ul",{},[1803,1804,1805,1806,1809],"li",{},"Zwei Vektoren sind genau dann abhängig, wenn sie ",[569,1807,1808],{},"kollinear"," sind, also Vielfache voneinander.",[1803,1811,1812,1813,1816,1817,1845],{},"Drei Vektoren sind genau dann abhängig, wenn sie ",[569,1814,1815],{},"komplanar"," sind, also in einer Ebene liegen. Das ist genau dann der Fall, wenn die Determinante der Matrix aus den drei Vektoren ",[574,1818,1820,1833],{"className":1819},[577],[574,1821,1823],{"className":1822},[581],[583,1824,1825],{"xmlns":585},[587,1826,1827,1831],{},[590,1828,1829],{},[608,1830,1135],{},[631,1832,1135],{"encoding":633},[574,1834,1836],{"className":1835,"ariaHidden":598},[638],[574,1837,1839,1842],{"className":1838},[642],[574,1840],{"className":1841,"style":1647},[646],[574,1843,1135],{"className":1844},[651]," ist.",[1803,1847,1848],{},"Vier oder mehr Vektoren im Raum sind immer linear abhängig.",[560,1850,1852],{"id":1851},"beispiele","Beispiele",[565,1854,1855,1856,1998,1999,2133,2134,2270,2271,2500],{},"Ist ",[574,1857,1859,1903],{"className":1858},[577],[574,1860,1862],{"className":1861},[581],[583,1863,1864],{"xmlns":585},[587,1865,1866,1900],{},[590,1867,1868,1874,1876,1880,1883,1885,1888,1890,1892,1894,1897],{},[596,1869,1870,1872],{"accent":598},[600,1871,867],{},[604,1873,606],{},[604,1875,1130],{},[604,1877,1879],{"stretchy":1878},"false","(",[608,1881,1882],{},"4",[604,1884,613],{"separator":598},[1139,1886,1887],{}," ",[608,1889,610],{},[604,1891,613],{"separator":598},[1139,1893,1887],{},[608,1895,1896],{},"7",[604,1898,1899],{"stretchy":1878},")",[631,1901,1902],{"encoding":633},"\\vec{v} = (4,\\ 1,\\ 7)",[574,1904,1906,1956],{"className":1905,"ariaHidden":598},[638],[574,1907,1909,1912,1947,1950,1953],{"className":1908},[642],[574,1910],{"className":1911,"style":668},[646],[574,1913,1915],{"className":1914},[651,655],[574,1916,1918],{"className":1917},[659],[574,1919,1921],{"className":1920},[663],[574,1922,1924,1932],{"className":1923,"style":668},[667],[574,1925,1926,1929],{"style":671},[574,1927],{"className":1928,"style":676},[675],[574,1930,867],{"className":1931,"style":902},[651,680],[574,1933,1934,1937],{"style":671},[574,1935],{"className":1936,"style":676},[675],[574,1938,1940],{"className":1939,"style":911},[689],[574,1941,1943],{"className":1942,"style":695},[694],[697,1944,1945],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,1946],{"d":708},[574,1948],{"className":1949,"style":1445},[762],[574,1951,1130],{"className":1952},[1449],[574,1954],{"className":1955,"style":1445},[762],[574,1957,1959,1963,1967,1970,1973,1976,1979,1982,1985,1988,1991,1994],{"className":1958},[642],[574,1960],{"className":1961,"style":1962},[646],"height:1em;vertical-align:-0.25em;",[574,1964,1879],{"className":1965},[1966],"mopen",[574,1968,1882],{"className":1969},[651],[574,1971,613],{"className":1972},[758],[574,1974,1887],{"className":1975},[762],[574,1977],{"className":1978,"style":763},[762],[574,1980,610],{"className":1981},[651],[574,1983,613],{"className":1984},[758],[574,1986,1887],{"className":1987},[762],[574,1989],{"className":1990,"style":763},[762],[574,1992,1896],{"className":1993},[651],[574,1995,1899],{"className":1996},[1997],"mclose"," eine Linearkombination von ",[574,2000,2002,2041],{"className":2001},[577],[574,2003,2005],{"className":2004},[581],[583,2006,2007],{"xmlns":585},[587,2008,2009,2038],{},[590,2010,2011,2017,2019,2021,2023,2025,2027,2029,2031,2033,2036],{},[596,2012,2013,2015],{"accent":598},[600,2014,602],{},[604,2016,606],{},[604,2018,1130],{},[604,2020,1879],{"stretchy":1878},[608,2022,610],{},[604,2024,613],{"separator":598},[1139,2026,1887],{},[608,2028,1135],{},[604,2030,613],{"separator":598},[1139,2032,1887],{},[608,2034,2035],{},"2",[604,2037,1899],{"stretchy":1878},[631,2039,2040],{"encoding":633},"\\vec{a} = (1,\\ 0,\\ 2)",[574,2042,2044,2094],{"className":2043,"ariaHidden":598},[638],[574,2045,2047,2050,2085,2088,2091],{"className":2046},[642],[574,2048],{"className":2049,"style":668},[646],[574,2051,2053],{"className":2052},[651,655],[574,2054,2056],{"className":2055},[659],[574,2057,2059],{"className":2058},[663],[574,2060,2062,2070],{"className":2061,"style":668},[667],[574,2063,2064,2067],{"style":671},[574,2065],{"className":2066,"style":676},[675],[574,2068,602],{"className":2069},[651,680],[574,2071,2072,2075],{"style":671},[574,2073],{"className":2074,"style":676},[675],[574,2076,2078],{"className":2077,"style":690},[689],[574,2079,2081],{"className":2080,"style":695},[694],[697,2082,2083],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,2084],{"d":708},[574,2086],{"className":2087,"style":1445},[762],[574,2089,1130],{"className":2090},[1449],[574,2092],{"className":2093,"style":1445},[762],[574,2095,2097,2100,2103,2106,2109,2112,2115,2118,2121,2124,2127,2130],{"className":2096},[642],[574,2098],{"className":2099,"style":1962},[646],[574,2101,1879],{"className":2102},[1966],[574,2104,610],{"className":2105},[651],[574,2107,613],{"className":2108},[758],[574,2110,1887],{"className":2111},[762],[574,2113],{"className":2114,"style":763},[762],[574,2116,1135],{"className":2117},[651],[574,2119,613],{"className":2120},[758],[574,2122,1887],{"className":2123},[762],[574,2125],{"className":2126,"style":763},[762],[574,2128,2035],{"className":2129},[651],[574,2131,1899],{"className":2132},[1997]," und ",[574,2135,2137,2176],{"className":2136},[577],[574,2138,2140],{"className":2139},[581],[583,2141,2142],{"xmlns":585},[587,2143,2144,2173],{},[590,2145,2146,2153,2155,2157,2159,2161,2163,2165,2167,2169,2171],{},[596,2147,2148,2151],{"accent":598},[600,2149,2150],{},"b",[604,2152,606],{},[604,2154,1130],{},[604,2156,1879],{"stretchy":1878},[608,2158,610],{},[604,2160,613],{"separator":598},[1139,2162,1887],{},[608,2164,610],{},[604,2166,613],{"separator":598},[1139,2168,1887],{},[608,2170,610],{},[604,2172,1899],{"stretchy":1878},[631,2174,2175],{"encoding":633},"\\vec{b} = (1,\\ 1,\\ 1)",[574,2177,2179,2231],{"className":2178,"ariaHidden":598},[638],[574,2180,2182,2186,2222,2225,2228],{"className":2181},[642],[574,2183],{"className":2184,"style":2185},[646],"height:0.9774em;",[574,2187,2189],{"className":2188},[651,655],[574,2190,2192],{"className":2191},[659],[574,2193,2195],{"className":2194},[663],[574,2196,2198,2206],{"className":2197,"style":2185},[667],[574,2199,2200,2203],{"style":671},[574,2201],{"className":2202,"style":676},[675],[574,2204,2150],{"className":2205},[651,680],[574,2207,2209,2212],{"style":2208},"top:-3.2634em;",[574,2210],{"className":2211,"style":676},[675],[574,2213,2215],{"className":2214,"style":690},[689],[574,2216,2218],{"className":2217,"style":695},[694],[697,2219,2220],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,2221],{"d":708},[574,2223],{"className":2224,"style":1445},[762],[574,2226,1130],{"className":2227},[1449],[574,2229],{"className":2230,"style":1445},[762],[574,2232,2234,2237,2240,2243,2246,2249,2252,2255,2258,2261,2264,2267],{"className":2233},[642],[574,2235],{"className":2236,"style":1962},[646],[574,2238,1879],{"className":2239},[1966],[574,2241,610],{"className":2242},[651],[574,2244,613],{"className":2245},[758],[574,2247,1887],{"className":2248},[762],[574,2250],{"className":2251,"style":763},[762],[574,2253,610],{"className":2254},[651],[574,2256,613],{"className":2257},[758],[574,2259,1887],{"className":2260},[762],[574,2262],{"className":2263,"style":763},[762],[574,2265,610],{"className":2266},[651],[574,2268,1899],{"className":2269},[1997],"? Aus ",[574,2272,2274,2318],{"className":2273},[577],[574,2275,2277],{"className":2276},[581],[583,2278,2279],{"xmlns":585},[587,2280,2281,2315],{},[590,2282,2283,2285,2288,2294,2296,2299,2301,2307,2309],{},[600,2284,936],{},[604,2286,2287],{},"⋅",[596,2289,2290,2292],{"accent":598},[600,2291,602],{},[604,2293,606],{},[604,2295,1107],{},[600,2297,2298],{},"s",[604,2300,2287],{},[596,2302,2303,2305],{"accent":598},[600,2304,2150],{},[604,2306,606],{},[604,2308,1130],{},[596,2310,2311,2313],{"accent":598},[600,2312,867],{},[604,2314,606],{},[631,2316,2317],{"encoding":633},"r \\cdot \\vec{a} + s \\cdot \\vec{b} = \\vec{v}",[574,2319,2321,2340,2391,2409,2459],{"className":2320,"ariaHidden":598},[638],[574,2322,2324,2328,2331,2334,2337],{"className":2323},[642],[574,2325],{"className":2326,"style":2327},[646],"height:0.4445em;",[574,2329,936],{"className":2330,"style":970},[651,680],[574,2332],{"className":2333,"style":1297},[762],[574,2335,2287],{"className":2336},[1301],[574,2338],{"className":2339,"style":1297},[762],[574,2341,2343,2347,2382,2385,2388],{"className":2342},[642],[574,2344],{"className":2345,"style":2346},[646],"height:0.7973em;vertical-align:-0.0833em;",[574,2348,2350],{"className":2349},[651,655],[574,2351,2353],{"className":2352},[659],[574,2354,2356],{"className":2355},[663],[574,2357,2359,2367],{"className":2358,"style":668},[667],[574,2360,2361,2364],{"style":671},[574,2362],{"className":2363,"style":676},[675],[574,2365,602],{"className":2366},[651,680],[574,2368,2369,2372],{"style":671},[574,2370],{"className":2371,"style":676},[675],[574,2373,2375],{"className":2374,"style":690},[689],[574,2376,2378],{"className":2377,"style":695},[694],[697,2379,2380],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,2381],{"d":708},[574,2383],{"className":2384,"style":1297},[762],[574,2386,1107],{"className":2387},[1301],[574,2389],{"className":2390,"style":1297},[762],[574,2392,2394,2397,2400,2403,2406],{"className":2393},[642],[574,2395],{"className":2396,"style":2327},[646],[574,2398,2298],{"className":2399},[651,680],[574,2401],{"className":2402,"style":1297},[762],[574,2404,2287],{"className":2405},[1301],[574,2407],{"className":2408,"style":1297},[762],[574,2410,2412,2415,2450,2453,2456],{"className":2411},[642],[574,2413],{"className":2414,"style":2185},[646],[574,2416,2418],{"className":2417},[651,655],[574,2419,2421],{"className":2420},[659],[574,2422,2424],{"className":2423},[663],[574,2425,2427,2435],{"className":2426,"style":2185},[667],[574,2428,2429,2432],{"style":671},[574,2430],{"className":2431,"style":676},[675],[574,2433,2150],{"className":2434},[651,680],[574,2436,2437,2440],{"style":2208},[574,2438],{"className":2439,"style":676},[675],[574,2441,2443],{"className":2442,"style":690},[689],[574,2444,2446],{"className":2445,"style":695},[694],[697,2447,2448],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,2449],{"d":708},[574,2451],{"className":2452,"style":1445},[762],[574,2454,1130],{"className":2455},[1449],[574,2457],{"className":2458,"style":1445},[762],[574,2460,2462,2465],{"className":2461},[642],[574,2463],{"className":2464,"style":668},[646],[574,2466,2468],{"className":2467},[651,655],[574,2469,2471],{"className":2470},[659],[574,2472,2474],{"className":2473},[663],[574,2475,2477,2485],{"className":2476,"style":668},[667],[574,2478,2479,2482],{"style":671},[574,2480],{"className":2481,"style":676},[675],[574,2483,867],{"className":2484,"style":902},[651,680],[574,2486,2487,2490],{"style":671},[574,2488],{"className":2489,"style":676},[675],[574,2491,2493],{"className":2492,"style":911},[689],[574,2494,2496],{"className":2495,"style":695},[694],[697,2497,2498],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,2499],{"d":708}," folgt:",[574,2502,2504],{"className":2503},[1075],[574,2505,2507,2600],{"className":2506},[577],[574,2508,2510],{"className":2509},[581],[583,2511,2512],{"xmlns":585,"display":1084},[587,2513,2514,2597],{},[2515,2516,2520,2549,2569],"mtable",{"rowspacing":2517,"columnalign":2518,"columnspacing":2519},"0.25em","right left","0em",[2521,2522,2523,2537],"mtr",{},[2524,2525,2526],"mtd",{},[2527,2528,2529],"mstyle",{"scriptlevel":1135,"displaystyle":598},[590,2530,2531,2533,2535],{},[600,2532,936],{},[604,2534,1107],{},[600,2536,2298],{},[2524,2538,2539],{},[2527,2540,2541],{"scriptlevel":1135,"displaystyle":598},[590,2542,2543,2545,2547],{},[590,2544],{},[604,2546,1130],{},[608,2548,1882],{},[2521,2550,2551,2557],{},[2524,2552,2553],{},[2527,2554,2555],{"scriptlevel":1135,"displaystyle":598},[600,2556,2298],{},[2524,2558,2559],{},[2527,2560,2561],{"scriptlevel":1135,"displaystyle":598},[590,2562,2563,2565,2567],{},[590,2564],{},[604,2566,1130],{},[608,2568,610],{},[2521,2570,2571,2585],{},[2524,2572,2573],{},[2527,2574,2575],{"scriptlevel":1135,"displaystyle":598},[590,2576,2577,2579,2581,2583],{},[608,2578,2035],{},[600,2580,936],{},[604,2582,1107],{},[600,2584,2298],{},[2524,2586,2587],{},[2527,2588,2589],{"scriptlevel":1135,"displaystyle":598},[590,2590,2591,2593,2595],{},[590,2592],{},[604,2594,1130],{},[608,2596,1896],{},[631,2598,2599],{"encoding":633},"\\begin{aligned}\nr + s &= 4 \\\\\ns &= 1 \\\\\n2r + s &= 7\n\\end{aligned}",[574,2601,2603],{"className":2602,"ariaHidden":598},[638],[574,2604,2606,2610],{"className":2605},[642],[574,2607],{"className":2608,"style":2609},[646],"height:4.2em;vertical-align:-1.85em;",[574,2611,2613],{"className":2612},[651],[574,2614,2616,2705],{"className":2615},[2515],[574,2617,2620],{"className":2618},[2619],"col-align-r",[574,2621,2623,2696],{"className":2622},[659,716],[574,2624,2626,2693],{"className":2625},[663],[574,2627,2630,2654,2666],{"className":2628,"style":2629},[667],"height:2.35em;",[574,2631,2633,2636],{"style":2632},"top:-4.51em;",[574,2634],{"className":2635,"style":676},[675],[574,2637,2639,2642,2645,2648,2651],{"className":2638},[651],[574,2640,936],{"className":2641,"style":970},[651,680],[574,2643],{"className":2644,"style":1297},[762],[574,2646,1107],{"className":2647},[1301],[574,2649],{"className":2650,"style":1297},[762],[574,2652,2298],{"className":2653},[651,680],[574,2655,2657,2660],{"style":2656},"top:-3.01em;",[574,2658],{"className":2659,"style":676},[675],[574,2661,2663],{"className":2662},[651],[574,2664,2298],{"className":2665},[651,680],[574,2667,2669,2672],{"style":2668},"top:-1.51em;",[574,2670],{"className":2671,"style":676},[675],[574,2673,2675,2678,2681,2684,2687,2690],{"className":2674},[651],[574,2676,2035],{"className":2677},[651],[574,2679,936],{"className":2680,"style":970},[651,680],[574,2682],{"className":2683,"style":1297},[762],[574,2685,1107],{"className":2686},[1301],[574,2688],{"className":2689,"style":1297},[762],[574,2691,2298],{"className":2692},[651,680],[574,2694,745],{"className":2695},[744],[574,2697,2699],{"className":2698},[663],[574,2700,2703],{"className":2701,"style":2702},[667],"height:1.85em;",[574,2704],{},[574,2706,2709],{"className":2707},[2708],"col-align-l",[574,2710,2712,2790],{"className":2711},[659,716],[574,2713,2715,2787],{"className":2714},[663],[574,2716,2718,2741,2764],{"className":2717,"style":2629},[667],[574,2719,2720,2723],{"style":2632},[574,2721],{"className":2722,"style":676},[675],[574,2724,2726,2729,2732,2735,2738],{"className":2725},[651],[574,2727],{"className":2728},[651],[574,2730],{"className":2731,"style":1445},[762],[574,2733,1130],{"className":2734},[1449],[574,2736],{"className":2737,"style":1445},[762],[574,2739,1882],{"className":2740},[651],[574,2742,2743,2746],{"style":2656},[574,2744],{"className":2745,"style":676},[675],[574,2747,2749,2752,2755,2758,2761],{"className":2748},[651],[574,2750],{"className":2751},[651],[574,2753],{"className":2754,"style":1445},[762],[574,2756,1130],{"className":2757},[1449],[574,2759],{"className":2760,"style":1445},[762],[574,2762,610],{"className":2763},[651],[574,2765,2766,2769],{"style":2668},[574,2767],{"className":2768,"style":676},[675],[574,2770,2772,2775,2778,2781,2784],{"className":2771},[651],[574,2773],{"className":2774},[651],[574,2776],{"className":2777,"style":1445},[762],[574,2779,1130],{"className":2780},[1449],[574,2782],{"className":2783,"style":1445},[762],[574,2785,1896],{"className":2786},[651],[574,2788,745],{"className":2789},[744],[574,2791,2793],{"className":2792},[663],[574,2794,2796],{"className":2795,"style":2702},[667],[574,2797],{},[565,2799,2800,2801,2133,2853,2905,2906,2981,2982,1064],{},"Aus den ersten beiden Zeilen folgt ",[574,2802,2804,2822],{"className":2803},[577],[574,2805,2807],{"className":2806},[581],[583,2808,2809],{"xmlns":585},[587,2810,2811,2819],{},[590,2812,2813,2815,2817],{},[600,2814,2298],{},[604,2816,1130],{},[608,2818,610],{},[631,2820,2821],{"encoding":633},"s = 1",[574,2823,2825,2844],{"className":2824,"ariaHidden":598},[638],[574,2826,2828,2832,2835,2838,2841],{"className":2827},[642],[574,2829],{"className":2830,"style":2831},[646],"height:0.4306em;",[574,2833,2298],{"className":2834},[651,680],[574,2836],{"className":2837,"style":1445},[762],[574,2839,1130],{"className":2840},[1449],[574,2842],{"className":2843,"style":1445},[762],[574,2845,2847,2850],{"className":2846},[642],[574,2848],{"className":2849,"style":1647},[646],[574,2851,610],{"className":2852},[651],[574,2854,2856,2875],{"className":2855},[577],[574,2857,2859],{"className":2858},[581],[583,2860,2861],{"xmlns":585},[587,2862,2863,2872],{},[590,2864,2865,2867,2869],{},[600,2866,936],{},[604,2868,1130],{},[608,2870,2871],{},"3",[631,2873,2874],{"encoding":633},"r = 3",[574,2876,2878,2896],{"className":2877,"ariaHidden":598},[638],[574,2879,2881,2884,2887,2890,2893],{"className":2880},[642],[574,2882],{"className":2883,"style":2831},[646],[574,2885,936],{"className":2886,"style":970},[651,680],[574,2888],{"className":2889,"style":1445},[762],[574,2891,1130],{"className":2892},[1449],[574,2894],{"className":2895,"style":1445},[762],[574,2897,2899,2902],{"className":2898},[642],[574,2900],{"className":2901,"style":1647},[646],[574,2903,2871],{"className":2904},[651],", die dritte passt mit ",[574,2907,2909,2932],{"className":2908},[577],[574,2910,2912],{"className":2911},[581],[583,2913,2914],{"xmlns":585},[587,2915,2916,2929],{},[590,2917,2918,2921,2923,2925,2927],{},[608,2919,2920],{},"6",[604,2922,1107],{},[608,2924,610],{},[604,2926,1130],{},[608,2928,1896],{},[631,2930,2931],{"encoding":633},"6 + 1 = 7",[574,2933,2935,2954,2972],{"className":2934,"ariaHidden":598},[638],[574,2936,2938,2942,2945,2948,2951],{"className":2937},[642],[574,2939],{"className":2940,"style":2941},[646],"height:0.7278em;vertical-align:-0.0833em;",[574,2943,2920],{"className":2944},[651],[574,2946],{"className":2947,"style":1297},[762],[574,2949,1107],{"className":2950},[1301],[574,2952],{"className":2953,"style":1297},[762],[574,2955,2957,2960,2963,2966,2969],{"className":2956},[642],[574,2958],{"className":2959,"style":1647},[646],[574,2961,610],{"className":2962},[651],[574,2964],{"className":2965,"style":1445},[762],[574,2967,1130],{"className":2968},[1449],[574,2970],{"className":2971,"style":1445},[762],[574,2973,2975,2978],{"className":2974},[642],[574,2976],{"className":2977,"style":1647},[646],[574,2979,1896],{"className":2980},[651],". Also ist ",[574,2983,2985,3021],{"className":2984},[577],[574,2986,2988],{"className":2987},[581],[583,2989,2990],{"xmlns":585},[587,2991,2992,3018],{},[590,2993,2994,3000,3002,3004,3010,3012],{},[596,2995,2996,2998],{"accent":598},[600,2997,867],{},[604,2999,606],{},[604,3001,1130],{},[608,3003,2871],{},[596,3005,3006,3008],{"accent":598},[600,3007,602],{},[604,3009,606],{},[604,3011,1107],{},[596,3013,3014,3016],{"accent":598},[600,3015,2150],{},[604,3017,606],{},[631,3019,3020],{"encoding":633},"\\vec{v} = 3\\vec{a} + \\vec{b}",[574,3022,3024,3074,3127],{"className":3023,"ariaHidden":598},[638],[574,3025,3027,3030,3065,3068,3071],{"className":3026},[642],[574,3028],{"className":3029,"style":668},[646],[574,3031,3033],{"className":3032},[651,655],[574,3034,3036],{"className":3035},[659],[574,3037,3039],{"className":3038},[663],[574,3040,3042,3050],{"className":3041,"style":668},[667],[574,3043,3044,3047],{"style":671},[574,3045],{"className":3046,"style":676},[675],[574,3048,867],{"className":3049,"style":902},[651,680],[574,3051,3052,3055],{"style":671},[574,3053],{"className":3054,"style":676},[675],[574,3056,3058],{"className":3057,"style":911},[689],[574,3059,3061],{"className":3060,"style":695},[694],[697,3062,3063],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3064],{"d":708},[574,3066],{"className":3067,"style":1445},[762],[574,3069,1130],{"className":3070},[1449],[574,3072],{"className":3073,"style":1445},[762],[574,3075,3077,3080,3083,3118,3121,3124],{"className":3076},[642],[574,3078],{"className":3079,"style":2346},[646],[574,3081,2871],{"className":3082},[651],[574,3084,3086],{"className":3085},[651,655],[574,3087,3089],{"className":3088},[659],[574,3090,3092],{"className":3091},[663],[574,3093,3095,3103],{"className":3094,"style":668},[667],[574,3096,3097,3100],{"style":671},[574,3098],{"className":3099,"style":676},[675],[574,3101,602],{"className":3102},[651,680],[574,3104,3105,3108],{"style":671},[574,3106],{"className":3107,"style":676},[675],[574,3109,3111],{"className":3110,"style":690},[689],[574,3112,3114],{"className":3113,"style":695},[694],[697,3115,3116],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3117],{"d":708},[574,3119],{"className":3120,"style":1297},[762],[574,3122,1107],{"className":3123},[1301],[574,3125],{"className":3126,"style":1297},[762],[574,3128,3130,3133],{"className":3129},[642],[574,3131],{"className":3132,"style":2185},[646],[574,3134,3136],{"className":3135},[651,655],[574,3137,3139],{"className":3138},[659],[574,3140,3142],{"className":3141},[663],[574,3143,3145,3153],{"className":3144,"style":2185},[667],[574,3146,3147,3150],{"style":671},[574,3148],{"className":3149,"style":676},[675],[574,3151,2150],{"className":3152},[651,680],[574,3154,3155,3158],{"style":2208},[574,3156],{"className":3157,"style":676},[675],[574,3159,3161],{"className":3160,"style":690},[689],[574,3162,3164],{"className":3163,"style":695},[694],[697,3165,3166],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3167],{"d":708},[565,3169,3170,3171,3236,3237,3236,3302,3366,3367,3613,3614,1064],{},"Damit sind ",[574,3172,3174,3192],{"className":3173},[577],[574,3175,3177],{"className":3176},[581],[583,3178,3179],{"xmlns":585},[587,3180,3181,3189],{},[590,3182,3183],{},[596,3184,3185,3187],{"accent":598},[600,3186,602],{},[604,3188,606],{},[631,3190,3191],{"encoding":633},"\\vec{a}",[574,3193,3195],{"className":3194,"ariaHidden":598},[638],[574,3196,3198,3201],{"className":3197},[642],[574,3199],{"className":3200,"style":668},[646],[574,3202,3204],{"className":3203},[651,655],[574,3205,3207],{"className":3206},[659],[574,3208,3210],{"className":3209},[663],[574,3211,3213,3221],{"className":3212,"style":668},[667],[574,3214,3215,3218],{"style":671},[574,3216],{"className":3217,"style":676},[675],[574,3219,602],{"className":3220},[651,680],[574,3222,3223,3226],{"style":671},[574,3224],{"className":3225,"style":676},[675],[574,3227,3229],{"className":3228,"style":690},[689],[574,3230,3232],{"className":3231,"style":695},[694],[697,3233,3234],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3235],{"d":708},", ",[574,3238,3240,3258],{"className":3239},[577],[574,3241,3243],{"className":3242},[581],[583,3244,3245],{"xmlns":585},[587,3246,3247,3255],{},[590,3248,3249],{},[596,3250,3251,3253],{"accent":598},[600,3252,2150],{},[604,3254,606],{},[631,3256,3257],{"encoding":633},"\\vec{b}",[574,3259,3261],{"className":3260,"ariaHidden":598},[638],[574,3262,3264,3267],{"className":3263},[642],[574,3265],{"className":3266,"style":2185},[646],[574,3268,3270],{"className":3269},[651,655],[574,3271,3273],{"className":3272},[659],[574,3274,3276],{"className":3275},[663],[574,3277,3279,3287],{"className":3278,"style":2185},[667],[574,3280,3281,3284],{"style":671},[574,3282],{"className":3283,"style":676},[675],[574,3285,2150],{"className":3286},[651,680],[574,3288,3289,3292],{"style":2208},[574,3290],{"className":3291,"style":676},[675],[574,3293,3295],{"className":3294,"style":690},[689],[574,3296,3298],{"className":3297,"style":695},[694],[697,3299,3300],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3301],{"d":708},[574,3303,3305,3322],{"className":3304},[577],[574,3306,3308],{"className":3307},[581],[583,3309,3310],{"xmlns":585},[587,3311,3312,3320],{},[590,3313,3314],{},[596,3315,3316,3318],{"accent":598},[600,3317,867],{},[604,3319,606],{},[631,3321,872],{"encoding":633},[574,3323,3325],{"className":3324,"ariaHidden":598},[638],[574,3326,3328,3331],{"className":3327},[642],[574,3329],{"className":3330,"style":668},[646],[574,3332,3334],{"className":3333},[651,655],[574,3335,3337],{"className":3336},[659],[574,3338,3340],{"className":3339},[663],[574,3341,3343,3351],{"className":3342,"style":668},[667],[574,3344,3345,3348],{"style":671},[574,3346],{"className":3347,"style":676},[675],[574,3349,867],{"className":3350,"style":902},[651,680],[574,3352,3353,3356],{"style":671},[574,3354],{"className":3355,"style":676},[675],[574,3357,3359],{"className":3358,"style":911},[689],[574,3360,3362],{"className":3361,"style":695},[694],[697,3363,3364],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3365],{"d":708}," linear abhängig, denn ",[574,3368,3370,3415],{"className":3369},[577],[574,3371,3373],{"className":3372},[581],[583,3374,3375],{"xmlns":585},[587,3376,3377,3412],{},[590,3378,3379,3381,3387,3389,3395,3398,3404,3406],{},[608,3380,2871],{},[596,3382,3383,3385],{"accent":598},[600,3384,602],{},[604,3386,606],{},[604,3388,1107],{},[596,3390,3391,3393],{"accent":598},[600,3392,2150],{},[604,3394,606],{},[604,3396,3397],{},"−",[596,3399,3400,3402],{"accent":598},[600,3401,867],{},[604,3403,606],{},[604,3405,1130],{},[596,3407,3408,3410],{"accent":598},[608,3409,1135],{},[604,3411,606],{},[631,3413,3414],{"encoding":633},"3\\vec{a} + \\vec{b} - \\vec{v} = \\vec{0}",[574,3416,3418,3471,3522,3572],{"className":3417,"ariaHidden":598},[638],[574,3419,3421,3424,3427,3462,3465,3468],{"className":3420},[642],[574,3422],{"className":3423,"style":2346},[646],[574,3425,2871],{"className":3426},[651],[574,3428,3430],{"className":3429},[651,655],[574,3431,3433],{"className":3432},[659],[574,3434,3436],{"className":3435},[663],[574,3437,3439,3447],{"className":3438,"style":668},[667],[574,3440,3441,3444],{"style":671},[574,3442],{"className":3443,"style":676},[675],[574,3445,602],{"className":3446},[651,680],[574,3448,3449,3452],{"style":671},[574,3450],{"className":3451,"style":676},[675],[574,3453,3455],{"className":3454,"style":690},[689],[574,3456,3458],{"className":3457,"style":695},[694],[697,3459,3460],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3461],{"d":708},[574,3463],{"className":3464,"style":1297},[762],[574,3466,1107],{"className":3467},[1301],[574,3469],{"className":3470,"style":1297},[762],[574,3472,3474,3478,3513,3516,3519],{"className":3473},[642],[574,3475],{"className":3476,"style":3477},[646],"height:1.0608em;vertical-align:-0.0833em;",[574,3479,3481],{"className":3480},[651,655],[574,3482,3484],{"className":3483},[659],[574,3485,3487],{"className":3486},[663],[574,3488,3490,3498],{"className":3489,"style":2185},[667],[574,3491,3492,3495],{"style":671},[574,3493],{"className":3494,"style":676},[675],[574,3496,2150],{"className":3497},[651,680],[574,3499,3500,3503],{"style":2208},[574,3501],{"className":3502,"style":676},[675],[574,3504,3506],{"className":3505,"style":690},[689],[574,3507,3509],{"className":3508,"style":695},[694],[697,3510,3511],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3512],{"d":708},[574,3514],{"className":3515,"style":1297},[762],[574,3517,3397],{"className":3518},[1301],[574,3520],{"className":3521,"style":1297},[762],[574,3523,3525,3528,3563,3566,3569],{"className":3524},[642],[574,3526],{"className":3527,"style":668},[646],[574,3529,3531],{"className":3530},[651,655],[574,3532,3534],{"className":3533},[659],[574,3535,3537],{"className":3536},[663],[574,3538,3540,3548],{"className":3539,"style":668},[667],[574,3541,3542,3545],{"style":671},[574,3543],{"className":3544,"style":676},[675],[574,3546,867],{"className":3547,"style":902},[651,680],[574,3549,3550,3553],{"style":671},[574,3551],{"className":3552,"style":676},[675],[574,3554,3556],{"className":3555,"style":911},[689],[574,3557,3559],{"className":3558,"style":695},[694],[697,3560,3561],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3562],{"d":708},[574,3564],{"className":3565,"style":1445},[762],[574,3567,1130],{"className":3568},[1449],[574,3570],{"className":3571,"style":1445},[762],[574,3573,3575,3578],{"className":3574},[642],[574,3576],{"className":3577,"style":1459},[646],[574,3579,3581],{"className":3580},[651,655],[574,3582,3584],{"className":3583},[659],[574,3585,3587],{"className":3586},[663],[574,3588,3590,3598],{"className":3589,"style":1459},[667],[574,3591,3592,3595],{"style":671},[574,3593],{"className":3594,"style":676},[675],[574,3596,1135],{"className":3597},[651],[574,3599,3600,3603],{"style":1482},[574,3601],{"className":3602,"style":676},[675],[574,3604,3606],{"className":3605,"style":690},[689],[574,3607,3609],{"className":3608,"style":695},[694],[697,3610,3611],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,3612],{"d":708},". Passend dazu ist die Determinante der Matrix mit diesen Spalten ",[574,3615,3617,3630],{"className":3616},[577],[574,3618,3620],{"className":3619},[581],[583,3621,3622],{"xmlns":585},[587,3623,3624,3628],{},[590,3625,3626],{},[608,3627,1135],{},[631,3629,1135],{"encoding":633},[574,3631,3633],{"className":3632,"ariaHidden":598},[638],[574,3634,3636,3639],{"className":3635},[642],[574,3637],{"className":3638,"style":1647},[646],[574,3640,1135],{"className":3641},[651],[565,3643,3644,3645,3236,3720,2133,3795,3870,3871,1064],{},"Die Vektoren 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0)",[574,3679,3681],{"className":3680,"ariaHidden":598},[638],[574,3682,3684,3687,3690,3693,3696,3699,3702,3705,3708,3711,3714,3717],{"className":3683},[642],[574,3685],{"className":3686,"style":1962},[646],[574,3688,1879],{"className":3689},[1966],[574,3691,610],{"className":3692},[651],[574,3694,613],{"className":3695},[758],[574,3697,1887],{"className":3698},[762],[574,3700],{"className":3701,"style":763},[762],[574,3703,1135],{"className":3704},[651],[574,3706,613],{"className":3707},[758],[574,3709,1887],{"className":3710},[762],[574,3712],{"className":3713,"style":763},[762],[574,3715,1135],{"className":3716},[651],[574,3718,1899],{"className":3719},[1997],[574,3721,3723,3753],{"className":3722},[577],[574,3724,3726],{"className":3725},[581],[583,3727,3728],{"xmlns":585},[587,3729,3730,3750],{},[590,3731,3732,3734,3736,3738,3740,3742,3744,3746,3748],{},[604,3733,1879],{"stretchy":1878},[608,3735,610],{},[604,3737,613],{"separator":598},[1139,3739,1887],{},[608,3741,610],{},[604,3743,613],{"separator":598},[1139,3745,1887],{},[608,3747,1135],{},[604,3749,1899],{"stretchy":1878},[631,3751,3752],{"encoding":633},"(1,\\ 1,\\ 0)",[574,3754,3756],{"className":3755,"ariaHidden":598},[638],[574,3757,3759,3762,3765,3768,3771,3774,3777,3780,3783,3786,3789,3792],{"className":3758},[642],[574,3760],{"className":3761,"style":1962},[646],[574,3763,1879],{"className":3764},[1966],[574,3766,610],{"className":3767},[651],[574,3769,613],{"className":3770},[758],[574,3772,1887],{"className":3773},[762],[574,3775],{"className":3776,"style":763},[762],[574,3778,610],{"className":3779},[651],[574,3781,613],{"className":3782},[758],[574,3784,1887],{"className":3785},[762],[574,3787],{"className":3788,"style":763},[762],[574,3790,1135],{"className":3791},[651],[574,3793,1899],{"className":3794},[1997],[574,3796,3798,3828],{"className":3797},[577],[574,3799,3801],{"className":3800},[581],[583,3802,3803],{"xmlns":585},[587,3804,3805,3825],{},[590,3806,3807,3809,3811,3813,3815,3817,3819,3821,3823],{},[604,3808,1879],{"stretchy":1878},[608,3810,610],{},[604,3812,613],{"separator":598},[1139,3814,1887],{},[608,3816,610],{},[604,3818,613],{"separator":598},[1139,3820,1887],{},[608,3822,610],{},[604,3824,1899],{"stretchy":1878},[631,3826,3827],{"encoding":633},"(1,\\ 1,\\ 1)",[574,3829,3831],{"className":3830,"ariaHidden":598},[638],[574,3832,3834,3837,3840,3843,3846,3849,3852,3855,3858,3861,3864,3867],{"className":3833},[642],[574,3835],{"className":3836,"style":1962},[646],[574,3838,1879],{"className":3839},[1966],[574,3841,610],{"className":3842},[651],[574,3844,613],{"className":3845},[758],[574,3847,1887],{"className":3848},[762],[574,3850],{"className":3851,"style":763},[762],[574,3853,610],{"className":3854},[651],[574,3856,613],{"className":3857},[758],[574,3859,1887],{"className":3860},[762],[574,3862],{"className":3863,"style":763},[762],[574,3865,610],{"className":3866},[651],[574,3868,1899],{"className":3869},[1997]," sind linear unabhängig: Die Determinante der Matrix mit diesen Spalten ist ",[574,3872,3874,3892],{"className":3873},[577],[574,3875,3877],{"className":3876},[581],[583,3878,3879],{"xmlns":585},[587,3880,3881,3889],{},[590,3882,3883,3885,3887],{},[608,3884,610],{},[604,3886,1676],{"mathvariant":1675},[608,3888,1135],{},[631,3890,3891],{"encoding":633},"1 \\neq 0",[574,3893,3895,3946],{"className":3894,"ariaHidden":598},[638],[574,3896,3898,3901,3904,3907,3943],{"className":3897},[642],[574,3899],{"className":3900,"style":1691},[646],[574,3902,610],{"className":3903},[651],[574,3905],{"className":3906,"style":1445},[762],[574,3908,3910,3937,3940],{"className":3909},[1449],[574,3911,3913],{"className":3912},[1449],[574,3914,3916],{"className":3915},[651,1745],[574,3917,3919],{"className":3918},[1749],[574,3920,3922,3925,3934],{"className":3921},[1753],[574,3923],{"className":3924,"style":1691},[646],[574,3926,3928],{"className":3927},[1760],[574,3929,3931],{"className":3930},[651],[574,3932,1767],{"className":3933},[1449],[574,3935],{"className":3936},[1771],[574,3938],{"className":3939},[762,1775],[574,3941,1130],{"className":3942},[1449],[574,3944],{"className":3945,"style":1445},[762],[574,3947,3949,3952],{"className":3948},[642],[574,3950],{"className":3951,"style":1647},[646],[574,3953,1135],{"className":3954},[651],[565,3956,3957,2133,4037,4122,4123,4308],{},[574,3958,3960,3992],{"className":3959},[577],[574,3961,3963],{"className":3962},[581],[583,3964,3965],{"xmlns":585},[587,3966,3967,3989],{},[590,3968,3969,3971,3973,3975,3977,3979,3981,3983,3985,3987],{},[604,3970,1879],{"stretchy":1878},[608,3972,2035],{},[604,3974,613],{"separator":598},[1139,3976,1887],{},[604,3978,3397],{},[608,3980,1882],{},[604,3982,613],{"separator":598},[1139,3984,1887],{},[608,3986,2920],{},[604,3988,1899],{"stretchy":1878},[631,3990,3991],{"encoding":633},"(2,\\ -4,\\ 6)",[574,3993,3995],{"className":3994,"ariaHidden":598},[638],[574,3996,3998,4001,4004,4007,4010,4013,4016,4019,4022,4025,4028,4031,4034],{"className":3997},[642],[574,3999],{"className":4000,"style":1962},[646],[574,4002,1879],{"className":4003},[1966],[574,4005,2035],{"className":4006},[651],[574,4008,613],{"className":4009},[758],[574,4011,1887],{"className":4012},[762],[574,4014],{"className":4015,"style":763},[762],[574,4017,3397],{"className":4018},[651],[574,4020,1882],{"className":4021},[651],[574,4023,613],{"className":4024},[758],[574,4026,1887],{"className":4027},[762],[574,4029],{"className":4030,"style":763},[762],[574,4032,2920],{"className":4033},[651],[574,4035,1899],{"className":4036},[1997],[574,4038,4040,4074],{"className":4039},[577],[574,4041,4043],{"className":4042},[581],[583,4044,4045],{"xmlns":585},[587,4046,4047,4071],{},[590,4048,4049,4051,4053,4055,4057,4059,4061,4063,4065,4067,4069],{},[604,4050,1879],{"stretchy":1878},[604,4052,3397],{},[608,4054,610],{},[604,4056,613],{"separator":598},[1139,4058,1887],{},[608,4060,2035],{},[604,4062,613],{"separator":598},[1139,4064,1887],{},[604,4066,3397],{},[608,4068,2871],{},[604,4070,1899],{"stretchy":1878},[631,4072,4073],{"encoding":633},"(-1,\\ 2,\\ -3)",[574,4075,4077],{"className":4076,"ariaHidden":598},[638],[574,4078,4080,4083,4086,4089,4092,4095,4098,4101,4104,4107,4110,4113,4116,4119],{"className":4079},[642],[574,4081],{"className":4082,"style":1962},[646],[574,4084,1879],{"className":4085},[1966],[574,4087,3397],{"className":4088},[651],[574,4090,610],{"className":4091},[651],[574,4093,613],{"className":4094},[758],[574,4096,1887],{"className":4097},[762],[574,4099],{"className":4100,"style":763},[762],[574,4102,2035],{"className":4103},[651],[574,4105,613],{"className":4106},[758],[574,4108,1887],{"className":4109},[762],[574,4111],{"className":4112,"style":763},[762],[574,4114,3397],{"className":4115},[651],[574,4117,2871],{"className":4118},[651],[574,4120,1899],{"className":4121},[1997]," sind kollinear, weil ",[574,4124,4126,4188],{"className":4125},[577],[574,4127,4129],{"className":4128},[581],[583,4130,4131],{"xmlns":585},[587,4132,4133,4185],{},[590,4134,4135,4137,4139,4141,4143,4145,4147,4149,4151,4153,4155,4157,4159,4161,4163,4165,4167,4169,4171,4173,4175,4177,4179,4181,4183],{},[604,4136,1879],{"stretchy":1878},[608,4138,2035],{},[604,4140,613],{"separator":598},[1139,4142,1887],{},[604,4144,3397],{},[608,4146,1882],{},[604,4148,613],{"separator":598},[1139,4150,1887],{},[608,4152,2920],{},[604,4154,1899],{"stretchy":1878},[604,4156,1130],{},[604,4158,3397],{},[608,4160,2035],{},[604,4162,2287],{},[604,4164,1879],{"stretchy":1878},[604,4166,3397],{},[608,4168,610],{},[604,4170,613],{"separator":598},[1139,4172,1887],{},[608,4174,2035],{},[604,4176,613],{"separator":598},[1139,4178,1887],{},[604,4180,3397],{},[608,4182,2871],{},[604,4184,1899],{"stretchy":1878},[631,4186,4187],{"encoding":633},"(2,\\ -4,\\ 6) = -2 \\cdot (-1,\\ 2,\\ -3)",[574,4189,4191,4242,4263],{"className":4190,"ariaHidden":598},[638],[574,4192,4194,4197,4200,4203,4206,4209,4212,4215,4218,4221,4224,4227,4230,4233,4236,4239],{"className":4193},[642],[574,4195],{"className":4196,"style":1962},[646],[574,4198,1879],{"className":4199},[1966],[574,4201,2035],{"className":4202},[651],[574,4204,613],{"className":4205},[758],[574,4207,1887],{"className":4208},[762],[574,4210],{"className":4211,"style":763},[762],[574,4213,3397],{"className":4214},[651],[574,4216,1882],{"className":4217},[651],[574,4219,613],{"className":4220},[758],[574,4222,1887],{"className":4223},[762],[574,4225],{"className":4226,"style":763},[762],[574,4228,2920],{"className":4229},[651],[574,4231,1899],{"className":4232},[1997],[574,4234],{"className":4235,"style":1445},[762],[574,4237,1130],{"className":4238},[1449],[574,4240],{"className":4241,"style":1445},[762],[574,4243,4245,4248,4251,4254,4257,4260],{"className":4244},[642],[574,4246],{"className":4247,"style":2941},[646],[574,4249,3397],{"className":4250},[651],[574,4252,2035],{"className":4253},[651],[574,4255],{"className":4256,"style":1297},[762],[574,4258,2287],{"className":4259},[1301],[574,4261],{"className":4262,"style":1297},[762],[574,4264,4266,4269,4272,4275,4278,4281,4284,4287,4290,4293,4296,4299,4302,4305],{"className":4265},[642],[574,4267],{"className":4268,"style":1962},[646],[574,4270,1879],{"className":4271},[1966],[574,4273,3397],{"className":4274},[651],[574,4276,610],{"className":4277},[651],[574,4279,613],{"className":4280},[758],[574,4282,1887],{"className":4283},[762],[574,4285],{"className":4286,"style":763},[762],[574,4288,2035],{"className":4289},[651],[574,4291,613],{"className":4292},[758],[574,4294,1887],{"className":4295},[762],[574,4297],{"className":4298,"style":763},[762],[574,4300,3397],{"className":4301},[651],[574,4303,2871],{"className":4304},[651],[574,4306,1899],{"className":4307},[1997],". Sie sind also linear abhängig.",[560,4310,4312],{"id":4311},"typische-fehler","Typische Fehler",[1800,4314,4315,4383,4386],{},[1803,4316,4317,4318,4382],{},"Nur zwei der drei Zeilen lösen. Erst wenn auch die dritte Zeile passt, ist ",[574,4319,4321,4338],{"className":4320},[577],[574,4322,4324],{"className":4323},[581],[583,4325,4326],{"xmlns":585},[587,4327,4328,4336],{},[590,4329,4330],{},[596,4331,4332,4334],{"accent":598},[600,4333,867],{},[604,4335,606],{},[631,4337,872],{"encoding":633},[574,4339,4341],{"className":4340,"ariaHidden":598},[638],[574,4342,4344,4347],{"className":4343},[642],[574,4345],{"className":4346,"style":668},[646],[574,4348,4350],{"className":4349},[651,655],[574,4351,4353],{"className":4352},[659],[574,4354,4356],{"className":4355},[663],[574,4357,4359,4367],{"className":4358,"style":668},[667],[574,4360,4361,4364],{"style":671},[574,4362],{"className":4363,"style":676},[675],[574,4365,867],{"className":4366,"style":902},[651,680],[574,4368,4369,4372],{"style":671},[574,4370],{"className":4371,"style":676},[675],[574,4373,4375],{"className":4374,"style":911},[689],[574,4376,4378],{"className":4377,"style":695},[694],[697,4379,4380],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,4381],{"d":708}," eine Linearkombination.",[1803,4384,4385],{},"Bei drei Vektoren prüfen, ob je zwei kollinear sind. Drei Vektoren können paarweise nicht kollinear und trotzdem abhängig sein, wie im ersten Beispiel.",[1803,4387,4388,4389,4454],{},"Den Nullvektor vergessen: Jede Menge von Vektoren, die ",[574,4390,4392,4410],{"className":4391},[577],[574,4393,4395],{"className":4394},[581],[583,4396,4397],{"xmlns":585},[587,4398,4399,4407],{},[590,4400,4401],{},[596,4402,4403,4405],{"accent":598},[608,4404,1135],{},[604,4406,606],{},[631,4408,4409],{"encoding":633},"\\vec{0}",[574,4411,4413],{"className":4412,"ariaHidden":598},[638],[574,4414,4416,4419],{"className":4415},[642],[574,4417],{"className":4418,"style":1459},[646],[574,4420,4422],{"className":4421},[651,655],[574,4423,4425],{"className":4424},[659],[574,4426,4428],{"className":4427},[663],[574,4429,4431,4439],{"className":4430,"style":1459},[667],[574,4432,4433,4436],{"style":671},[574,4434],{"className":4435,"style":676},[675],[574,4437,1135],{"className":4438},[651],[574,4440,4441,4444],{"style":1482},[574,4442],{"className":4443,"style":676},[675],[574,4445,4447],{"className":4446,"style":690},[689],[574,4448,4450],{"className":4449,"style":695},[694],[697,4451,4452],{"xmlns":699,"width":700,"height":701,"style":702,"viewBox":703,"preserveAspectRatio":704},[706,4453],{"d":708}," enthält, ist linear abhängig.",{"title":4456,"searchDepth":4457,"depth":4457,"links":4458},"",2,[4459,4460,4461],{"id":562,"depth":4457,"text":563},{"id":1851,"depth":4457,"text":1852},{"id":4311,"depth":4457,"text":4312},[4463,4468,4471,4474,4476,4478,4480,4482,4485],{"lhs":4464,"rhs":1882,"where":4465},"r*1 + s*1",{"r":4466,"s":4467},3,1,{"lhs":4469,"rhs":610,"where":4470},"r*0 + s*1",{"r":4466,"s":4467},{"lhs":4472,"rhs":1896,"where":4473},"r*2 + s*1",{"r":4466,"s":4467},{"lhs":4475,"rhs":1135},"det([[1, 1, 4], [0, 1, 1], [2, 1, 7]])",{"lhs":4477,"rhs":1135},"1*(1*7 - 1*1) - 1*(0*7 - 1*2) + 4*(0*1 - 1*2)",{"lhs":4479,"rhs":610},"det([[1, 1, 1], [0, 1, 1], [0, 0, 1]])",{"lhs":4481,"rhs":2035},"-2*(-1)",{"lhs":4483,"rhs":4484},"-2*2","-4",{"lhs":4486,"rhs":2920},"-2*(-3)","r_1, \\ldots, r_n \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_1, \\ldots, r_n \\in \\mathbb{R}\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:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;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\">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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\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:0.15em;\">\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","linear-combination","\\vec{v} = r_1 \\vec{a}_1 + r_2 \\vec{a}_2 + \\ldots + r_n \\vec{a}_n","\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>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{v} = r_1 \\vec{a}_1 + r_2 \\vec{a}_2 + \\ldots + r_n \\vec{a}_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:0.714em;\">\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\" style=\"margin-right:0.0359em;\">v\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:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t 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