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Sie sind genau dann linear unabhängig, wenn ",[568,1099,1101,1134],{"className":1100},[571],[568,1102,1104],{"className":1103},[575],[577,1105,1106],{"xmlns":579},[581,1107,1108,1131],{},[584,1109,1110,1114,1117,1121,1123,1126,1129],{},[594,1111,1113],{"mathvariant":1112},"normal","rg",[598,1115,1116],{},"⁡",[598,1118,1120],{"stretchy":1119},"false","(",[594,1122,1081],{},[598,1124,1125],{"stretchy":1119},")",[598,1127,1128],{},"=",[594,1130,623],{},[625,1132,1133],{"encoding":627},"\\operatorname{rg}(A) = k",[568,1135,1137,1175],{"className":1136,"ariaHidden":592},[632],[568,1138,1140,1144,1153,1157,1160,1164,1168,1172],{"className":1139},[636],[568,1141],{"className":1142,"style":1143},[640],"height:1em;vertical-align:-0.25em;",[568,1145,1148],{"className":1146},[1147],"mop",[568,1149,1113],{"className":1150,"style":1152},[645,1151],"mathrm","margin-right:0.0139em;",[568,1154,1120],{"className":1155},[1156],"mopen",[568,1158,1081],{"className":1159},[645,674],[568,1161,1125],{"className":1162},[1163],"mclose",[568,1165],{"className":1166,"style":1167},[757],"margin-right:0.2778em;",[568,1169,1128],{"className":1170},[1171],"mrel",[568,1173],{"className":1174,"style":1167},[757],[568,1176,1178,1182],{"className":1177},[636],[568,1179],{"className":1180,"style":1181},[640],"height:0.6944em;",[568,1183,623],{"className":1184,"style":834},[645,674],".",[1064,1187,1188,1189,1241,1242,1185],{},"Bei ",[568,1190,1192,1210],{"className":1191},[571],[568,1193,1195],{"className":1194},[575],[577,1196,1197],{"xmlns":579},[581,1198,1199,1207],{},[584,1200,1201,1203,1205],{},[594,1202,623],{},[598,1204,1128],{},[594,1206,1013],{},[625,1208,1209],{"encoding":627},"k = n",[568,1211,1213,1231],{"className":1212,"ariaHidden":592},[632],[568,1214,1216,1219,1222,1225,1228],{"className":1215},[636],[568,1217],{"className":1218,"style":1181},[640],[568,1220,623],{"className":1221,"style":834},[645,674],[568,1223],{"className":1224,"style":1167},[757],[568,1226,1128],{"className":1227},[1171],[568,1229],{"className":1230,"style":1167},[757],[568,1232,1234,1238],{"className":1233},[636],[568,1235],{"className":1236,"style":1237},[640],"height:0.4306em;",[568,1239,1013],{"className":1240},[645,674]," Vektoren (quadratische Matrix): linear unabhängig ",[568,1243,1245,1278],{"className":1244},[571],[568,1246,1248],{"className":1247},[575],[577,1249,1250],{"xmlns":579},[581,1251,1252,1275],{},[584,1253,1254,1258,1261,1263,1266,1268,1270,1273],{},[1255,1256,1257],"mtext",{},"  ",[598,1259,1260],{},"⟺",[1255,1262,1257],{},[594,1264,1265],{},"det",[598,1267,1116],{},[594,1269,1081],{},[598,1271,1272],{"mathvariant":1112},"≠",[602,1274,870],{},[625,1276,1277],{"encoding":627},"\\iff \\det A \\neq 0",[568,1279,1281,1300,1365],{"className":1280,"ariaHidden":592},[632],[568,1282,1284,1288,1291,1294,1297],{"className":1283},[636],[568,1285],{"className":1286,"style":1287},[640],"height:0.549em;vertical-align:-0.024em;",[568,1289],{"className":1290,"style":1167},[757],[568,1292,1260],{"className":1293},[1171],[568,1295],{"className":1296,"style":1167},[757],[568,1298],{"className":1299,"style":1167},[757],[568,1301,1303,1307,1310,1313,1316,1319,1362],{"className":1302},[636],[568,1304],{"className":1305,"style":1306},[640],"height:0.8889em;vertical-align:-0.1944em;",[568,1308,1265],{"className":1309},[1147],[568,1311],{"className":1312,"style":758},[757],[568,1314,1081],{"className":1315},[645,674],[568,1317],{"className":1318,"style":1167},[757],[568,1320,1322,1355,1359],{"className":1321},[1171],[568,1323,1325],{"className":1324},[1171],[568,1326,1329],{"className":1327},[645,1328],"vbox",[568,1330,1333],{"className":1331},[1332],"thinbox",[568,1334,1337,1340,1351],{"className":1335},[1336],"rlap",[568,1338],{"className":1339,"style":1306},[640],[568,1341,1344],{"className":1342},[1343],"inner",[568,1345,1347],{"className":1346},[645],[568,1348,1350],{"className":1349},[1171],"",[568,1352],{"className":1353},[1354],"fix",[568,1356],{"className":1357},[757,1358],"nobreak",[568,1360,1128],{"className":1361},[1171],[568,1363],{"className":1364,"style":1167},[757],[568,1366,1368,1371],{"className":1367},[636],[568,1369],{"className":1370,"style":882},[640],[568,1372,870],{"className":1373},[645],[1064,1375,1376,1377,1405,1406,1464],{},"Mehr als ",[568,1378,1380,1393],{"className":1379},[571],[568,1381,1383],{"className":1382},[575],[577,1384,1385],{"xmlns":579},[581,1386,1387,1391],{},[584,1388,1389],{},[594,1390,1013],{},[625,1392,1013],{"encoding":627},[568,1394,1396],{"className":1395,"ariaHidden":592},[632],[568,1397,1399,1402],{"className":1398},[636],[568,1400],{"className":1401,"style":1237},[640],[568,1403,1013],{"className":1404},[645,674]," Vektoren im ",[568,1407,1409,1426],{"className":1408},[571],[568,1410,1412],{"className":1411},[575],[577,1413,1414],{"xmlns":579},[581,1415,1416,1424],{},[584,1417,1418],{},[1005,1419,1420,1422],{},[594,1421,1010],{"mathvariant":1009},[594,1423,1013],{},[625,1425,1016],{"encoding":627},[568,1427,1429],{"className":1428,"ariaHidden":592},[632],[568,1430,1432,1435],{"className":1431},[636],[568,1433],{"className":1434,"style":1026},[640],[568,1436,1438,1441],{"className":1437},[645],[568,1439,1010],{"className":1440},[645,1033],[568,1442,1444],{"className":1443},[707],[568,1445,1447],{"className":1446},[653],[568,1448,1450],{"className":1449},[657],[568,1451,1453],{"className":1452,"style":1046},[661],[568,1454,1455,1458],{"style":1049},[568,1456],{"className":1457,"style":725},[669],[568,1459,1461],{"className":1460},[729,730,731,732],[568,1462,1013],{"className":1463},[645,674,732]," sind immer linear abhängig.",[1064,1466,1467],{},"Eine Menge, die den Nullvektor enthält, ist immer linear abhängig.",[564,1469,1470,1471,1474],{},"Linear unabhängige Vektoren, die den ganzen Raum erzeugen, bilden eine ",[848,1472,1473],{},"Basis",". Die Definition gilt in jedem Vektorraum, auch für Polynome oder Funktionen.",[559,1476,1478],{"id":1477},"beispiele","Beispiele",[564,1480,1481,1482,1558,1559,1558,1634,1709],{},"Die Vektoren ",[568,1483,1485,1516],{"className":1484},[571],[568,1486,1488],{"className":1487},[575],[577,1489,1490],{"xmlns":579},[581,1491,1492,1513],{},[584,1493,1494,1496,1498,1500,1503,1505,1507,1509,1511],{},[598,1495,1120],{"stretchy":1119},[602,1497,604],{},[598,1499,607],{"separator":592},[1255,1501,1502],{}," ",[602,1504,870],{},[598,1506,607],{"separator":592},[1255,1508,1502],{},[602,1510,604],{},[598,1512,1125],{"stretchy":1119},[625,1514,1515],{"encoding":627},"(1,\\ 0,\\ 1)",[568,1517,1519],{"className":1518,"ariaHidden":592},[632],[568,1520,1522,1525,1528,1531,1534,1537,1540,1543,1546,1549,1552,1555],{"className":1521},[636],[568,1523],{"className":1524,"style":1143},[640],[568,1526,1120],{"className":1527},[1156],[568,1529,604],{"className":1530},[645],[568,1532,607],{"className":1533},[753],[568,1535,1502],{"className":1536},[757],[568,1538],{"className":1539,"style":758},[757],[568,1541,870],{"className":1542},[645],[568,1544,607],{"className":1545},[753],[568,1547,1502],{"className":1548},[757],[568,1550],{"className":1551,"style":758},[757],[568,1553,604],{"className":1554},[645],[568,1556,1125],{"className":1557},[1163],", ",[568,1560,1562,1592],{"className":1561},[571],[568,1563,1565],{"className":1564},[575],[577,1566,1567],{"xmlns":579},[581,1568,1569,1589],{},[584,1570,1571,1573,1575,1577,1579,1581,1583,1585,1587],{},[598,1572,1120],{"stretchy":1119},[602,1574,870],{},[598,1576,607],{"separator":592},[1255,1578,1502],{},[602,1580,604],{},[598,1582,607],{"separator":592},[1255,1584,1502],{},[602,1586,604],{},[598,1588,1125],{"stretchy":1119},[625,1590,1591],{"encoding":627},"(0,\\ 1,\\ 1)",[568,1593,1595],{"className":1594,"ariaHidden":592},[632],[568,1596,1598,1601,1604,1607,1610,1613,1616,1619,1622,1625,1628,1631],{"className":1597},[636],[568,1599],{"className":1600,"style":1143},[640],[568,1602,1120],{"className":1603},[1156],[568,1605,870],{"className":1606},[645],[568,1608,607],{"className":1609},[753],[568,1611,1502],{"className":1612},[757],[568,1614],{"className":1615,"style":758},[757],[568,1617,604],{"className":1618},[645],[568,1620,607],{"className":1621},[753],[568,1623,1502],{"className":1624},[757],[568,1626],{"className":1627,"style":758},[757],[568,1629,604],{"className":1630},[645],[568,1632,1125],{"className":1633},[1163],[568,1635,1637,1667],{"className":1636},[571],[568,1638,1640],{"className":1639},[575],[577,1641,1642],{"xmlns":579},[581,1643,1644,1664],{},[584,1645,1646,1648,1650,1652,1654,1656,1658,1660,1662],{},[598,1647,1120],{"stretchy":1119},[602,1649,604],{},[598,1651,607],{"separator":592},[1255,1653,1502],{},[602,1655,604],{},[598,1657,607],{"separator":592},[1255,1659,1502],{},[602,1661,870],{},[598,1663,1125],{"stretchy":1119},[625,1665,1666],{"encoding":627},"(1,\\ 1,\\ 0)",[568,1668,1670],{"className":1669,"ariaHidden":592},[632],[568,1671,1673,1676,1679,1682,1685,1688,1691,1694,1697,1700,1703,1706],{"className":1672},[636],[568,1674],{"className":1675,"style":1143},[640],[568,1677,1120],{"className":1678},[1156],[568,1680,604],{"className":1681},[645],[568,1683,607],{"className":1684},[753],[568,1686,1502],{"className":1687},[757],[568,1689],{"className":1690,"style":758},[757],[568,1692,604],{"className":1693},[645],[568,1695,607],{"className":1696},[753],[568,1698,1502],{"className":1699},[757],[568,1701],{"className":1702,"style":758},[757],[568,1704,870],{"className":1705},[645],[568,1707,1125],{"className":1708},[1163]," als Spalten ergeben",[568,1711,1714],{"className":1712},[1713],"katex-display",[568,1715,1717,1860],{"className":1716},[571],[568,1718,1720],{"className":1719},[575],[577,1721,1723],{"xmlns":579,"display":1722},"block",[581,1724,1725,1857],{},[584,1726,1727,1729,1731,1806,1808,1810,1813,1815,1817,1820,1822,1824,1826,1828,1831,1833,1835,1837,1839,1841,1843,1845,1847,1849,1852,1854],{},[594,1728,1265],{},[598,1730,1116],{},[584,1732,1733,1735,1804],{},[598,1734,1120],{"fence":592},[1736,1737,1741,1764,1784],"mtable",{"rowspacing":1738,"columnalign":1739,"columnspacing":1740},"0.16em","center center center","1em",[1742,1743,1744,1752,1758],"mtr",{},[1745,1746,1747],"mtd",{},[1748,1749,1750],"mstyle",{"scriptlevel":870,"displaystyle":1119},[602,1751,604],{},[1745,1753,1754],{},[1748,1755,1756],{"scriptlevel":870,"displaystyle":1119},[602,1757,870],{},[1745,1759,1760],{},[1748,1761,1762],{"scriptlevel":870,"displaystyle":1119},[602,1763,604],{},[1742,1765,1766,1772,1778],{},[1745,1767,1768],{},[1748,1769,1770],{"scriptlevel":870,"displaystyle":1119},[602,1771,870],{},[1745,1773,1774],{},[1748,1775,1776],{"scriptlevel":870,"displaystyle":1119},[602,1777,604],{},[1745,1779,1780],{},[1748,1781,1782],{"scriptlevel":870,"displaystyle":1119},[602,1783,604],{},[1742,1785,1786,1792,1798],{},[1745,1787,1788],{},[1748,1789,1790],{"scriptlevel":870,"displaystyle":1119},[602,1791,604],{},[1745,1793,1794],{},[1748,1795,1796],{"scriptlevel":870,"displaystyle":1119},[602,1797,604],{},[1745,1799,1800],{},[1748,1801,1802],{"scriptlevel":870,"displaystyle":1119},[602,1803,870],{},[598,1805,1125],{"fence":592},[598,1807,1128],{},[602,1809,604],{},[598,1811,1812],{},"⋅",[598,1814,1120],{"stretchy":1119},[602,1816,870],{},[598,1818,1819],{},"−",[602,1821,604],{},[598,1823,1125],{"stretchy":1119},[598,1825,1819],{},[602,1827,870],{},[598,1829,1830],{},"+",[602,1832,604],{},[598,1834,1812],{},[598,1836,1120],{"stretchy":1119},[602,1838,870],{},[598,1840,1819],{},[602,1842,604],{},[598,1844,1125],{"stretchy":1119},[598,1846,1128],{},[598,1848,1819],{},[602,1850,1851],{},"2",[598,1853,1272],{"mathvariant":1112},[602,1855,1856],{},"0.",[625,1858,1859],{"encoding":627},"\\det \\begin{pmatrix} 1 & 0 & 1 \\\\ 0 & 1 & 1 \\\\ 1 & 1 & 0 \\end{pmatrix} = 1 \\cdot (0 - 1) - 0 + 1 \\cdot (0 - 1) = -2 \\neq 0.",[568,1861,1863,2166,2186,2207,2228,2247,2265,2286,2307,2361],{"className":1862,"ariaHidden":592},[632],[568,1864,1866,1870,1873,1876,2157,2160,2163],{"className":1865},[636],[568,1867],{"className":1868,"style":1869},[640],"height:3.6em;vertical-align:-1.55em;",[568,1871,1265],{"className":1872},[1147],[568,1874],{"className":1875,"style":758},[757],[568,1877,1879,1927,2119],{"className":1878},[762],[568,1880,1882],{"className":1881},[1156],[568,1883,1887],{"className":1884},[1885,1886],"delimsizing","mult",[568,1888,1890,1918],{"className":1889},[653,711],[568,1891,1893,1915],{"className":1892},[657],[568,1894,1897],{"className":1895,"style":1896},[661],"height:2.05em;",[568,1898,1900,1904],{"style":1899},"top:-4.05em;",[568,1901],{"className":1902,"style":1903},[669],"height:5.6em;",[568,1905,1907],{"style":1906},"width:0.875em;height:3.6em;",[692,1908,1912],{"xmlns":694,"width":1909,"height":1910,"viewBox":1911},"0.875em","3.6em","0 0 875 3600",[701,1913],{"d":1914},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 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\\cdot (1,\\ 2,\\ 3) - 2 \\cdot (4,\\ 5,\\ 6) + 1 \\cdot (7,\\ 8,\\ 9) = (0,\\ 0,\\ 0)",[568,2774,2776,2794,2842,2860,2908,2926,2974],{"className":2775,"ariaHidden":592},[632],[568,2777,2779,2782,2785,2788,2791],{"className":2778},[636],[568,2780],{"className":2781,"style":882},[640],[568,2783,604],{"className":2784},[645],[568,2786],{"className":2787,"style":2178},[757],[568,2789,1812],{"className":2790},[2182],[568,2792],{"className":2793,"style":2178},[757],[568,2795,2797,2800,2803,2806,2809,2812,2815,2818,2821,2824,2827,2830,2833,2836,2839],{"className":2796},[636],[568,2798],{"className":2799,"style":1143},[640],[568,2801,1120],{"className":2802},[1156],[568,2804,604],{"className":2805},[645],[568,2807,607],{"className":2808},[753],[568,2810,1502],{"className":2811},[757],[568,2813],{"className":2814,"style":758},[757],[568,2816,1851],{"className":2817},[645],[568,2819,607],{"className":2820},[753],[568,2822,1502],{"className":2823},[757],[568,2825],{"className":2826,"style":758},[757],[568,2828,2391],{"className":2829},[645],[568,2831,1125],{"className":2832},[1163],[568,2834],{"className":2835,"style":2178},[757],[568,2837,1819],{"className":2838},[2182],[568,2840],{"className":2841,"style":2178},[757],[568,2843,2845,2848,2851,2854,2857],{"className":2844},[636],[568,2846],{"className":2847,"style":882},[640],[568,2849,1851],{"className":2850},[645],[568,2852],{"className":2853,"style":2178},[757],[568,2855,1812],{"className":2856},[2182],[568,2858],{"className":2859,"style":2178},[757],[568,2861,2863,2866,2869,2872,2875,2878,2881,2884,2887,2890,2893,2896,2899,2902,2905],{"className":2862},[636],[568,2864],{"className":2865,"style":1143},[640],[568,2867,1120],{"className":2868},[1156],[568,2870,2527],{"className":2871},[645],[568,2873,607],{"className":2874},[753],[568,2876,1502],{"className":2877},[757],[568,2879],{"className":2880,"style":758},[757],[568,2882,2534],{"className":2883},[645],[568,2885,607],{"className":2886},[753],[568,2888,1502],{"className":2889},[757],[568,2891],{"className":2892,"style":758},[757],[568,2894,2541],{"className":2895},[645],[568,2897,1125],{"className":2898},[1163],[568,2900],{"className":2901,"style":2178},[757],[568,2903,1830],{"className":2904},[2182],[568,2906],{"className":2907,"style":2178},[757],[568,2909,2911,2914,2917,2920,2923],{"className":2910},[636],[568,2912],{"className":2913,"style":882},[640],[568,2915,604],{"className":2916},[645],[568,2918],{"className":2919,"style":2178},[757],[568,2921,1812],{"className":2922},[2182],[568,2924],{"className":2925,"style":2178},[757],[568,2927,2929,2932,2935,2938,2941,2944,2947,2950,2953,2956,2959,2962,2965,2968,2971],{"className":2928},[636],[568,2930],{"className":2931,"style":1143},[640],[568,2933,1120],{"className":2934},[1156],[568,2936,2605],{"className":2937},[645],[568,2939,607],{"className":2940},[753],[568,2942,1502],{"className":2943},[757],[568,2945],{"className":2946,"style":758},[757],[568,2948,2612],{"className":2949},[645],[568,2951,607],{"className":2952},[753],[568,2954,1502],{"className":2955},[757],[568,2957],{"className":2958,"style":758},[757],[568,2960,2619],{"className":2961},[645],[568,2963,1125],{"className":2964},[1163],[568,2966],{"className":2967,"style":1167},[757],[568,2969,1128],{"className":2970},[1171],[568,2972],{"className":2973,"style":1167},[757],[568,2975,2977,2980,2983,2986,2989,2992,2995,2998,3001,3004,3007,3010],{"className":2976},[636],[568,2978],{"className":2979,"style":1143},[640],[568,2981,1120],{"className":2982},[1156],[568,2984,870],{"className":2985},[645],[568,2987,607],{"className":2988},[753],[568,2990,1502],{"className":2991},[757],[568,2993],{"className":2994,"style":758},[757],[568,2996,870],{"className":2997},[645],[568,2999,607],{"className":3000},[753],[568,3002,1502],{"className":3003},[757],[568,3005],{"className":3006,"style":758},[757],[568,3008,870],{"className":3009},[645],[568,3011,1125],{"className":3012},[1163],". Passend dazu ist die Determinante der Spaltenmatrix ",[568,3015,3017,3030],{"className":3016},[571],[568,3018,3020],{"className":3019},[575],[577,3021,3022],{"xmlns":579},[581,3023,3024,3028],{},[584,3025,3026],{},[602,3027,870],{},[625,3029,870],{"encoding":627},[568,3031,3033],{"className":3032,"ariaHidden":592},[632],[568,3034,3036,3039],{"className":3035},[636],[568,3037],{"className":3038,"style":882},[640],[568,3040,870],{"className":3041},[645],[564,3043,3044,3045,1558,3073,1558,3102,3161,3162,3302,3303,3331,3332,1558,3383,3434,3435,3491,3492,3852,3853,3937,3938,4033],{},"Die Polynome ",[568,3046,3048,3061],{"className":3047},[571],[568,3049,3051],{"className":3050},[575],[577,3052,3053],{"xmlns":579},[581,3054,3055,3059],{},[584,3056,3057],{},[602,3058,604],{},[625,3060,604],{"encoding":627},[568,3062,3064],{"className":3063,"ariaHidden":592},[632],[568,3065,3067,3070],{"className":3066},[636],[568,3068],{"className":3069,"style":882},[640],[568,3071,604],{"className":3072},[645],[568,3074,3076,3090],{"className":3075},[571],[568,3077,3079],{"className":3078},[575],[577,3080,3081],{"xmlns":579},[581,3082,3083,3088],{},[584,3084,3085],{},[594,3086,3087],{},"x",[625,3089,3087],{"encoding":627},[568,3091,3093],{"className":3092,"ariaHidden":592},[632],[568,3094,3096,3099],{"className":3095},[636],[568,3097],{"className":3098,"style":1237},[640],[568,3100,3087],{"className":3101},[645,674],[568,3103,3105,3123],{"className":3104},[571],[568,3106,3108],{"className":3107},[575],[577,3109,3110],{"xmlns":579},[581,3111,3112,3120],{},[584,3113,3114],{},[1005,3115,3116,3118],{},[594,3117,3087],{},[602,3119,1851],{},[625,3121,3122],{"encoding":627},"x^2",[568,3124,3126],{"className":3125,"ariaHidden":592},[632],[568,3127,3129,3132],{"className":3128},[636],[568,3130],{"className":3131,"style":2404},[640],[568,3133,3135,3138],{"className":3134},[645],[568,3136,3087],{"className":3137},[645,674],[568,3139,3141],{"className":3140},[707],[568,3142,3144],{"className":3143},[653],[568,3145,3147],{"className":3146},[657],[568,3148,3150],{"className":3149,"style":2404},[661],[568,3151,3152,3155],{"style":1049},[568,3153],{"className":3154,"style":725},[669],[568,3156,3158],{"className":3157},[729,730,731,732],[568,3159,1851],{"className":3160},[645,732]," sind linear unabhängig: Gilt ",[568,3163,3165,3202],{"className":3164},[571],[568,3166,3168],{"className":3167},[575],[577,3169,3170],{"xmlns":579},[581,3171,3172,3199],{},[584,3173,3174,3177,3179,3182,3184,3186,3189,3195,3197],{},[594,3175,3176],{},"a",[598,3178,1830],{},[594,3180,3181],{},"b",[594,3183,3087],{},[598,3185,1830],{},[594,3187,3188],{},"c",[1005,3190,3191,3193],{},[594,3192,3087],{},[602,3194,1851],{},[598,3196,1128],{},[602,3198,870],{},[625,3200,3201],{"encoding":627},"a + bx + cx^2 = 0",[568,3203,3205,3224,3246,3293],{"className":3204,"ariaHidden":592},[632],[568,3206,3208,3212,3215,3218,3221],{"className":3207},[636],[568,3209],{"className":3210,"style":3211},[640],"height:0.6667em;vertical-align:-0.0833em;",[568,3213,3176],{"className":3214},[645,674],[568,3216],{"className":3217,"style":2178},[757],[568,3219,1830],{"className":3220},[2182],[568,3222],{"className":3223,"style":2178},[757],[568,3225,3227,3231,3234,3237,3240,3243],{"className":3226},[636],[568,3228],{"className":3229,"style":3230},[640],"height:0.7778em;vertical-align:-0.0833em;",[568,3232,3181],{"className":3233},[645,674],[568,3235,3087],{"className":3236},[645,674],[568,3238],{"className":3239,"style":2178},[757],[568,3241,1830],{"className":3242},[2182],[568,3244],{"className":3245,"style":2178},[757],[568,3247,3249,3252,3255,3284,3287,3290],{"className":3248},[636],[568,3250],{"className":3251,"style":2404},[640],[568,3253,3188],{"className":3254},[645,674],[568,3256,3258,3261],{"className":3257},[645],[568,3259,3087],{"className":3260},[645,674],[568,3262,3264],{"className":3263},[707],[568,3265,3267],{"className":3266},[653],[568,3268,3270],{"className":3269},[657],[568,3271,3273],{"className":3272,"style":2404},[661],[568,3274,3275,3278],{"style":1049},[568,3276],{"className":3277,"style":725},[669],[568,3279,3281],{"className":3280},[729,730,731,732],[568,3282,1851],{"className":3283},[645,732],[568,3285],{"className":3286,"style":1167},[757],[568,3288,1128],{"className":3289},[1171],[568,3291],{"className":3292,"style":1167},[757],[568,3294,3296,3299],{"className":3295},[636],[568,3297],{"className":3298,"style":882},[640],[568,3300,870],{"className":3301},[645]," für alle ",[568,3304,3306,3319],{"className":3305},[571],[568,3307,3309],{"className":3308},[575],[577,3310,3311],{"xmlns":579},[581,3312,3313,3317],{},[584,3314,3315],{},[594,3316,3087],{},[625,3318,3087],{"encoding":627},[568,3320,3322],{"className":3321,"ariaHidden":592},[632],[568,3323,3325,3328],{"className":3324},[636],[568,3326],{"className":3327,"style":1237},[640],[568,3329,3087],{"className":3330},[645,674],", dann liefern ",[568,3333,3335,3353],{"className":3334},[571],[568,3336,3338],{"className":3337},[575],[577,3339,3340],{"xmlns":579},[581,3341,3342,3350],{},[584,3343,3344,3346,3348],{},[594,3345,3087],{},[598,3347,1128],{},[602,3349,870],{},[625,3351,3352],{"encoding":627},"x = 0",[568,3354,3356,3374],{"className":3355,"ariaHidden":592},[632],[568,3357,3359,3362,3365,3368,3371],{"className":3358},[636],[568,3360],{"className":3361,"style":1237},[640],[568,3363,3087],{"className":3364},[645,674],[568,3366],{"className":3367,"style":1167},[757],[568,3369,1128],{"className":3370},[1171],[568,3372],{"className":3373,"style":1167},[757],[568,3375,3377,3380],{"className":3376},[636],[568,3378],{"className":3379,"style":882},[640],[568,3381,870],{"className":3382},[645],[568,3384,3386,3404],{"className":3385},[571],[568,3387,3389],{"className":3388},[575],[577,3390,3391],{"xmlns":579},[581,3392,3393,3401],{},[584,3394,3395,3397,3399],{},[594,3396,3087],{},[598,3398,1128],{},[602,3400,604],{},[625,3402,3403],{"encoding":627},"x = 1",[568,3405,3407,3425],{"className":3406,"ariaHidden":592},[632],[568,3408,3410,3413,3416,3419,3422],{"className":3409},[636],[568,3411],{"className":3412,"style":1237},[640],[568,3414,3087],{"className":3415},[645,674],[568,3417],{"className":3418,"style":1167},[757],[568,3420,1128],{"className":3421},[1171],[568,3423],{"className":3424,"style":1167},[757],[568,3426,3428,3431],{"className":3427},[636],[568,3429],{"className":3430,"style":882},[640],[568,3432,604],{"className":3433},[645]," und ",[568,3436,3438,3458],{"className":3437},[571],[568,3439,3441],{"className":3440},[575],[577,3442,3443],{"xmlns":579},[581,3444,3445,3455],{},[584,3446,3447,3449,3451,3453],{},[594,3448,3087],{},[598,3450,1128],{},[598,3452,1819],{},[602,3454,604],{},[625,3456,3457],{"encoding":627},"x = -1",[568,3459,3461,3479],{"className":3460,"ariaHidden":592},[632],[568,3462,3464,3467,3470,3473,3476],{"className":3463},[636],[568,3465],{"className":3466,"style":1237},[640],[568,3468,3087],{"className":3469},[645,674],[568,3471],{"className":3472,"style":1167},[757],[568,3474,1128],{"className":3475},[1171],[568,3477],{"className":3478,"style":1167},[757],[568,3480,3482,3485,3488],{"className":3481},[636],[568,3483],{"className":3484,"style":2234},[640],[568,3486,1819],{"className":3487},[645],[568,3489,604],{"className":3490},[645]," ein System mit der Koeffizientenmatrix ",[568,3493,3495,3577],{"className":3494},[571],[568,3496,3498],{"className":3497},[575],[577,3499,3500],{"xmlns":579},[581,3501,3502,3574],{},[584,3503,3504,3506,3572],{},[598,3505,1120],{"fence":592},[1736,3507,3508,3528,3548],{"rowspacing":1738,"columnalign":1739,"columnspacing":1740},[1742,3509,3510,3516,3522],{},[1745,3511,3512],{},[1748,3513,3514],{"scriptlevel":870,"displaystyle":1119},[602,3515,604],{},[1745,3517,3518],{},[1748,3519,3520],{"scriptlevel":870,"displaystyle":1119},[602,3521,870],{},[1745,3523,3524],{},[1748,3525,3526],{"scriptlevel":870,"displaystyle":1119},[602,3527,870],{},[1742,3529,3530,3536,3542],{},[1745,3531,3532],{},[1748,3533,3534],{"scriptlevel":870,"displaystyle":1119},[602,3535,604],{},[1745,3537,3538],{},[1748,3539,3540],{"scriptlevel":870,"displaystyle":1119},[602,3541,604],{},[1745,3543,3544],{},[1748,3545,3546],{"scriptlevel":870,"displaystyle":1119},[602,3547,604],{},[1742,3549,3550,3556,3566],{},[1745,3551,3552],{},[1748,3553,3554],{"scriptlevel":870,"displaystyle":1119},[602,3555,604],{},[1745,3557,3558],{},[1748,3559,3560],{"scriptlevel":870,"displaystyle":1119},[584,3561,3562,3564],{},[598,3563,1819],{},[602,3565,604],{},[1745,3567,3568],{},[1748,3569,3570],{"scriptlevel":870,"displaystyle":1119},[602,3571,604],{},[598,3573,1125],{"fence":592},[625,3575,3576],{"encoding":627},"\\begin{pmatrix} 1 & 0 & 0 \\\\ 1 & 1 & 1 \\\\ 1 & -1 & 1 \\end{pmatrix}",[568,3578,3580],{"className":3579,"ariaHidden":592},[632],[568,3581,3583,3586],{"className":3582},[636],[568,3584],{"className":3585,"style":1869},[640],[568,3587,3589,3626,3815],{"className":3588},[762],[568,3590,3592],{"className":3591},[1156],[568,3593,3595],{"className":3594},[1885,1886],[568,3596,3598,3618],{"className":3597},[653,711],[568,3599,3601,3615],{"className":3600},[657],[568,3602,3604],{"className":3603,"style":1896},[661],[568,3605,3606,3609],{"style":1899},[568,3607],{"className":3608,"style":1903},[669],[568,3610,3611],{"style":1906},[692,3612,3613],{"xmlns":694,"width":1909,"height":1910,"viewBox":1911},[701,3614],{"d":1914},[568,3616,740],{"className":3617},[739],[568,3619,3621],{"className":3620},[657],[568,3622,3624],{"className":3623,"style":1924},[661],[568,3625],{},[568,3627,3629],{"className":3628},[645],[568,3630,3632,3688,3691,3694,3753,3756,3759],{"className":3631},[1736],[568,3633,3635],{"className":3634},[1936],[568,3636,3638,3680],{"className":3637},[653,711],[568,3639,3641,3677],{"className":3640},[657],[568,3642,3644,3655,3666],{"className":3643,"style":1896},[661],[568,3645,3646,3649],{"style":1948},[568,3647],{"className":3648,"style":670},[669],[568,3650,3652],{"className":3651},[645],[568,3653,604],{"className":3654},[645],[568,3656,3657,3660],{"style":1960},[568,3658],{"className":3659,"style":670},[669],[568,3661,3663],{"className":3662},[645],[568,3664,604],{"className":3665},[645],[568,3667,3668,3671],{"style":1972},[568,3669],{"className":3670,"style":670},[669],[568,3672,3674],{"className":3673},[645],[568,3675,604],{"className":3676},[645],[568,3678,740],{"className":3679},[739],[568,3681,3683],{"className":3682},[657],[568,3684,3686],{"className":3685,"style":1924},[661],[568,3687],{},[568,3689],{"className":3690,"style":1997},[1996],[568,3692],{"className":3693,"style":1997},[1996],[568,3695,3697],{"className":3696},[1936],[568,3698,3700,3745],{"className":3699},[653,711],[568,3701,3703,3742],{"className":3702},[657],[568,3704,3706,3717,3728],{"className":3705,"style":1896},[661],[568,3707,3708,3711],{"style":1948},[568,3709],{"className":3710,"style":670},[669],[568,3712,3714],{"className":3713},[645],[568,3715,870],{"className":3716},[645],[568,3718,3719,3722],{"style":1960},[568,3720],{"className":3721,"style":670},[669],[568,3723,3725],{"className":3724},[645],[568,3726,604],{"className":3727},[645],[568,3729,3730,3733],{"style":1972},[568,3731],{"className":3732,"style":670},[669],[568,3734,3736,3739],{"className":3735},[645],[568,3737,1819],{"className":3738},[645],[568,3740,604],{"className":3741},[645],[568,3743,740],{"className":3744},[739],[568,3746,3748],{"className":3747},[657],[568,3749,3751],{"className":3750,"style":1924},[661],[568,3752],{},[568,3754],{"className":3755,"style":1997},[1996],[568,3757],{"className":3758,"style":1997},[1996],[568,3760,3762],{"className":3761},[1936],[568,3763,3765,3807],{"className":3764},[653,711],[568,3766,3768,3804],{"className":3767},[657],[568,3769,3771,3782,3793],{"className":3770,"style":1896},[661],[568,3772,3773,3776],{"style":1948},[568,3774],{"className":3775,"style":670},[669],[568,3777,3779],{"className":3778},[645],[568,3780,870],{"className":3781},[645],[568,3783,3784,3787],{"style":1960},[568,3785],{"className":3786,"style":670},[669],[568,3788,3790],{"className":3789},[645],[568,3791,604],{"className":3792},[645],[568,3794,3795,3798],{"style":1972},[568,3796],{"className":3797,"style":670},[669],[568,3799,3801],{"className":3800},[645],[568,3802,604],{"className":3803},[645],[568,3805,740],{"className":3806},[739],[568,3808,3810],{"className":3809},[657],[568,3811,3813],{"className":3812,"style":1924},[661],[568,3814],{},[568,3816,3818],{"className":3817},[1163],[568,3819,3821],{"className":3820},[1885,1886],[568,3822,3824,3844],{"className":3823},[653,711],[568,3825,3827,3841],{"className":3826},[657],[568,3828,3830],{"className":3829,"style":1896},[661],[568,3831,3832,3835],{"style":1899},[568,3833],{"className":3834,"style":1903},[669],[568,3836,3837],{"style":1906},[692,3838,3839],{"xmlns":694,"width":1909,"height":1910,"viewBox":1911},[701,3840],{"d":2145},[568,3842,740],{"className":3843},[739],[568,3845,3847],{"className":3846},[657],[568,3848,3850],{"className":3849,"style":1924},[661],[568,3851],{},". Ihre Determinante ist ",[568,3854,3856,3874],{"className":3855},[571],[568,3857,3859],{"className":3858},[575],[577,3860,3861],{"xmlns":579},[581,3862,3863,3871],{},[584,3864,3865,3867,3869],{},[602,3866,1851],{},[598,3868,1272],{"mathvariant":1112},[602,3870,870],{},[625,3872,3873],{"encoding":627},"2 \\neq 0",[568,3875,3877,3928],{"className":3876,"ariaHidden":592},[632],[568,3878,3880,3883,3886,3889,3925],{"className":3879},[636],[568,3881],{"className":3882,"style":1306},[640],[568,3884,1851],{"className":3885},[645],[568,3887],{"className":3888,"style":1167},[757],[568,3890,3892,3919,3922],{"className":3891},[1171],[568,3893,3895],{"className":3894},[1171],[568,3896,3898],{"className":3897},[645,1328],[568,3899,3901],{"className":3900},[1332],[568,3902,3904,3907,3916],{"className":3903},[1336],[568,3905],{"className":3906,"style":1306},[640],[568,3908,3910],{"className":3909},[1343],[568,3911,3913],{"className":3912},[645],[568,3914,1350],{"className":3915},[1171],[568,3917],{"className":3918},[1354],[568,3920],{"className":3921},[757,1358],[568,3923,1128],{"className":3924},[1171],[568,3926],{"className":3927,"style":1167},[757],[568,3929,3931,3934],{"className":3930},[636],[568,3932],{"className":3933,"style":882},[640],[568,3935,870],{"className":3936},[645],", also ist nur ",[568,3939,3941,3967],{"className":3940},[571],[568,3942,3944],{"className":3943},[575],[577,3945,3946],{"xmlns":579},[581,3947,3948,3964],{},[584,3949,3950,3952,3954,3956,3958,3960,3962],{},[594,3951,3176],{},[598,3953,1128],{},[594,3955,3181],{},[598,3957,1128],{},[594,3959,3188],{},[598,3961,1128],{},[602,3963,870],{},[625,3965,3966],{"encoding":627},"a = b = c = 0",[568,3968,3970,3988,4006,4024],{"className":3969,"ariaHidden":592},[632],[568,3971,3973,3976,3979,3982,3985],{"className":3972},[636],[568,3974],{"className":3975,"style":1237},[640],[568,3977,3176],{"className":3978},[645,674],[568,3980],{"className":3981,"style":1167},[757],[568,3983,1128],{"className":3984},[1171],[568,3986],{"className":3987,"style":1167},[757],[568,3989,3991,3994,3997,4000,4003],{"className":3990},[636],[568,3992],{"className":3993,"style":1181},[640],[568,3995,3181],{"className":3996},[645,674],[568,3998],{"className":3999,"style":1167},[757],[568,4001,1128],{"className":4002},[1171],[568,4004],{"className":4005,"style":1167},[757],[568,4007,4009,4012,4015,4018,4021],{"className":4008},[636],[568,4010],{"className":4011,"style":1237},[640],[568,4013,3188],{"className":4014},[645,674],[568,4016],{"className":4017,"style":1167},[757],[568,4019,1128],{"className":4020},[1171],[568,4022],{"className":4023,"style":1167},[757],[568,4025,4027,4030],{"className":4026},[636],[568,4028],{"className":4029,"style":882},[640],[568,4031,870],{"className":4032},[645]," möglich.",[559,4035,4037],{"id":4036},"typische-fehler","Typische Fehler",[1061,4039,4040,4043,4177],{},[1064,4041,4042],{},"Nur prüfen, ob je zwei Vektoren Vielfache voneinander sind. Drei Vektoren können paarweise unabhängig und trotzdem linear abhängig sein, wie im zweiten Beispiel.",[1064,4044,4045,4046,3302,4143,4172,4173,4176],{},"Die Implikation umdrehen: Dass ",[568,4047,4049,4073],{"className":4048},[571],[568,4050,4052],{"className":4051},[575],[577,4053,4054],{"xmlns":579},[581,4055,4056,4070],{},[584,4057,4058,4066,4068],{},[587,4059,4060,4063],{},[594,4061,4062],{},"λ",[594,4064,4065],{},"i",[598,4067,1128],{},[602,4069,870],{},[625,4071,4072],{"encoding":627},"\\lambda_i = 0",[568,4074,4076,4134],{"className":4075,"ariaHidden":592},[632],[568,4077,4079,4083,4125,4128,4131],{"className":4078},[636],[568,4080],{"className":4081,"style":4082},[640],"height:0.8444em;vertical-align:-0.15em;",[568,4084,4086,4089],{"className":4085},[645],[568,4087,4062],{"className":4088},[645,674],[568,4090,4092],{"className":4091},[707],[568,4093,4095,4117],{"className":4094},[653,711],[568,4096,4098,4114],{"className":4097},[657],[568,4099,4102],{"className":4100,"style":4101},[661],"height:0.3117em;",[568,4103,4105,4108],{"style":4104},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[568,4106],{"className":4107,"style":725},[669],[568,4109,4111],{"className":4110},[729,730,731,732],[568,4112,4065],{"className":4113},[645,674,732],[568,4115,740],{"className":4116},[739],[568,4118,4120],{"className":4119},[657],[568,4121,4123],{"className":4122,"style":747},[661],[568,4124],{},[568,4126],{"className":4127,"style":1167},[757],[568,4129,1128],{"className":4130},[1171],[568,4132],{"className":4133,"style":1167},[757],[568,4135,4137,4140],{"className":4136},[636],[568,4138],{"className":4139,"style":882},[640],[568,4141,870],{"className":4142},[645],[568,4144,4146,4159],{"className":4145},[571],[568,4147,4149],{"className":4148},[575],[577,4150,4151],{"xmlns":579},[581,4152,4153,4157],{},[584,4154,4155],{},[594,4156,4065],{},[625,4158,4065],{"encoding":627},[568,4160,4162],{"className":4161,"ariaHidden":592},[632],[568,4163,4165,4169],{"className":4164},[636],[568,4166],{"className":4167,"style":4168},[640],"height:0.6595em;",[568,4170,4065],{"className":4171},[645,674]," den Nullvektor ergibt, gilt immer. Gezeigt werden muss, dass ",[848,4174,4175],{},"nur"," diese Wahl ihn ergibt.",[1064,4178,4179,4180,4264,4265,4323],{},"Das Determinantenkriterium auf ",[568,4181,4183,4201],{"className":4182},[571],[568,4184,4186],{"className":4185},[575],[577,4187,4188],{"xmlns":579},[581,4189,4190,4198],{},[584,4191,4192,4194,4196],{},[594,4193,623],{},[598,4195,1272],{"mathvariant":1112},[594,4197,1013],{},[625,4199,4200],{"encoding":627},"k \\neq n",[568,4202,4204,4255],{"className":4203,"ariaHidden":592},[632],[568,4205,4207,4210,4213,4216,4252],{"className":4206},[636],[568,4208],{"className":4209,"style":1306},[640],[568,4211,623],{"className":4212,"style":834},[645,674],[568,4214],{"className":4215,"style":1167},[757],[568,4217,4219,4246,4249],{"className":4218},[1171],[568,4220,4222],{"className":4221},[1171],[568,4223,4225],{"className":4224},[645,1328],[568,4226,4228],{"className":4227},[1332],[568,4229,4231,4234,4243],{"className":4230},[1336],[568,4232],{"className":4233,"style":1306},[640],[568,4235,4237],{"className":4236},[1343],[568,4238,4240],{"className":4239},[645],[568,4241,1350],{"className":4242},[1171],[568,4244],{"className":4245},[1354],[568,4247],{"className":4248},[757,1358],[568,4250,1128],{"className":4251},[1171],[568,4253],{"className":4254,"style":1167},[757],[568,4256,4258,4261],{"className":4257},[636],[568,4259],{"className":4260,"style":1237},[640],[568,4262,1013],{"className":4263},[645,674]," Vektoren anwenden. Für zwei Vektoren im ",[568,4266,4268,4285],{"className":4267},[571],[568,4269,4271],{"className":4270},[575],[577,4272,4273],{"xmlns":579},[581,4274,4275,4283],{},[584,4276,4277],{},[1005,4278,4279,4281],{},[594,4280,1010],{"mathvariant":1009},[602,4282,2391],{},[625,4284,2394],{"encoding":627},[568,4286,4288],{"className":4287,"ariaHidden":592},[632],[568,4289,4291,4294],{"className":4290},[636],[568,4292],{"className":4293,"style":2404},[640],[568,4295,4297,4300],{"className":4296},[645],[568,4298,1010],{"className":4299},[645,1033],[568,4301,4303],{"className":4302},[707],[568,4304,4306],{"className":4305},[653],[568,4307,4309],{"className":4308},[657],[568,4310,4312],{"className":4311,"style":2404},[661],[568,4313,4314,4317],{"style":1049},[568,4315],{"className":4316,"style":725},[669],[568,4318,4320],{"className":4319},[729,730,731,732],[568,4321,2391],{"className":4322},[645,732]," gibt es keine Determinante, dort hilft der Rang.",{"title":4325,"searchDepth":4326,"depth":4326,"links":4327},"",2,[4328,4329,4330],{"id":561,"depth":4326,"text":562},{"id":1477,"depth":4326,"text":1478},{"id":4036,"depth":4326,"text":4037},[4332,4335,4337,4339,4341,4343,4345],{"lhs":4333,"rhs":4334},"det([[1, 0, 1], [0, 1, 1], [1, 1, 0]])","-2",{"lhs":4336,"rhs":4334},"1*(1*0 - 1*1) - 0 + 1*(0*1 - 1*1)",{"lhs":4338,"rhs":870},"1 - 2*4 + 7",{"lhs":4340,"rhs":870},"2 - 2*5 + 8",{"lhs":4342,"rhs":870},"3 - 2*6 + 9",{"lhs":4344,"rhs":870},"det([[1, 4, 7], [2, 5, 8], [3, 6, 9]])",{"lhs":4346,"rhs":1851},"det([[1, 0, 0], [1, 1, 1], [1, -1, 1]])","\\vec v_1, \\ldots, \\vec v_k \\in V,\\ \\lambda_1, \\ldots, \\lambda_k \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec v_1, \\ldots, \\vec v_k \\in V,\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:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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=\"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:-0.0359em;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 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=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;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\" style=\"margin-right:0.0315em;\">k\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\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>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lambda_1, \\ldots, \\lambda_k \\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">λ\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: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\">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\">λ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\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 mathnormal mtight\" style=\"margin-right:0.0315em;\">k\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-independence","\\lambda_1 \\vec v_1 + \\lambda_2 \\vec v_2 + \\ldots + \\lambda_k \\vec v_k = \\vec 0 \\;\\Longrightarrow\\; \\lambda_1 = \\lambda_2 = \\ldots = \\lambda_k = 0","\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>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟹\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lambda_1 \\vec v_1 + \\lambda_2 \\vec v_2 + \\ldots + \\lambda_k \\vec v_k = \\vec 0 \\;\\Longrightarrow\\; \\lambda_1 = \\lambda_2 = \\ldots = \\lambda_k = 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:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">λ\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: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\">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=\"mord\">\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=\"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:-0.0359em;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=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">λ\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: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\">2\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=\"mord\">\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=\"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:-0.0359em;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\">2\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:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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