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A",[572,1097,1099,1156],{"className":1098,"ariaHidden":602},[601],[572,1100,1102,1105,1145,1149,1153],{"className":1101},[606],[572,1103],{"className":1104,"style":770},[610],[572,1106,1108,1111],{"className":1107},[615],[572,1109,754],{"className":1110},[615,616],[572,1112,1114],{"className":1113},[780],[572,1115,1117,1137],{"className":1116},[784,785],[572,1118,1120,1134],{"className":1119},[789],[572,1121,1123],{"className":1122,"style":794},[793],[572,1124,1125,1128],{"style":797},[572,1126],{"className":1127,"style":802},[801],[572,1129,1131],{"className":1130},[806,807,808,809],[572,1132,757],{"className":1133},[615,616,809],[572,1135,817],{"className":1136},[816],[572,1138,1140],{"className":1139},[789],[572,1141,1143],{"className":1142,"style":824},[793],[572,1144],{},[572,1146],{"className":1147,"style":1148},[696],"margin-right:0.2778em;",[572,1150,1072],{"className":1151},[1152],"mrel",[572,1154],{"className":1155,"style":1148},[696],[572,1157,1159,1163,1166,1169,1209,1212,1215,1218,1221],{"className":1158},[606],[572,1160],{"className":1161,"style":1162},[610],"height:1em;vertical-align:-0.25em;",[572,1164,668],{"className":1165},[692],[572,1167],{"className":1168,"style":697},[696],[572,1170,1172,1175],{"className":1171},[615],[572,1173,675],{"className":1174},[615,616],[572,1176,1178],{"className":1177},[780],[572,1179,1181,1201],{"className":1180},[784,785],[572,1182,1184,1198],{"className":1183},[789],[572,1185,1187],{"className":1186,"style":794},[793],[572,1188,1189,1192],{"style":797},[572,1190],{"className":1191,"style":802},[801],[572,1193,1195],{"className":1194},[806,807,808,809],[572,1196,757],{"className":1197},[615,616,809],[572,1199,817],{"className":1200},[816],[572,1202,1204],{"className":1203},[789],[572,1205,1207],{"className":1206,"style":824},[793],[572,1208],{},[572,1210,1086],{"className":1211},[615],[572,1213],{"className":1214,"style":697},[696],[572,1216,668],{"className":1217},[692],[572,1219],{"className":1220,"style":697},[696],[572,1222,675],{"className":1223},[615,616],".",[564,1226,1227,1228,1284,1285,1337],{},"Die Regel ist vor allem für ",[572,1229,1231,1251],{"className":1230},[575],[572,1232,1234],{"className":1233},[579],[581,1235,1236],{"xmlns":583},[585,1237,1238,1248],{},[588,1239,1240,1243,1246],{},[715,1241,1242],{},"2",[670,1244,1245],{},"×",[715,1247,1242],{},[595,1249,1250],{"encoding":597},"2 \\times 2",[572,1252,1254,1275],{"className":1253,"ariaHidden":602},[601],[572,1255,1257,1261,1264,1268,1272],{"className":1256},[606],[572,1258],{"className":1259,"style":1260},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,1262,1242],{"className":1263},[615],[572,1265],{"className":1266,"style":1267},[696],"margin-right:0.2222em;",[572,1269,1245],{"className":1270},[1271],"mbin",[572,1273],{"className":1274,"style":1267},[696],[572,1276,1278,1281],{"className":1277},[606],[572,1279],{"className":1280,"style":729},[610],[572,1282,1242],{"className":1283},[615],"- und ",[572,1286,1288,1307],{"className":1287},[575],[572,1289,1291],{"className":1290},[579],[581,1292,1293],{"xmlns":583},[585,1294,1295,1304],{},[588,1296,1297,1300,1302],{},[715,1298,1299],{},"3",[670,1301,1245],{},[715,1303,1299],{},[595,1305,1306],{"encoding":597},"3 \\times 3",[572,1308,1310,1328],{"className":1309,"ariaHidden":602},[601],[572,1311,1313,1316,1319,1322,1325],{"className":1312},[606],[572,1314],{"className":1315,"style":1260},[610],[572,1317,1299],{"className":1318},[615],[572,1320],{"className":1321,"style":1267},[696],[572,1323,1245],{"className":1324},[1271],[572,1326],{"className":1327,"style":1267},[696],[572,1329,1331,1334],{"className":1330},[606],[572,1332],{"className":1333,"style":729},[610],[572,1335,1299],{"className":1336},[615],"-Systeme praktisch und für theoretische Aussagen nützlich (z.B. dass die Lösung stetig von den Koeffizienten abhängt). Für große Systeme ist das Gauß-Verfahren deutlich weniger Rechenaufwand.",[559,1339,1341],{"id":1340},"beispiele","Beispiele",[564,1343,1344,1508,1509,1672],{},[572,1345,1347,1381],{"className":1346},[575],[572,1348,1350],{"className":1349},[579],[581,1351,1352],{"xmlns":583},[585,1353,1354,1378],{},[588,1355,1356,1358,1365,1368,1374,1376],{},[715,1357,1242],{},[750,1359,1360,1362],{},[591,1361,754],{},[715,1363,1364],{},"1",[670,1366,1367],{},"−",[750,1369,1370,1372],{},[591,1371,754],{},[715,1373,1242],{},[670,1375,1072],{},[715,1377,1364],{},[595,1379,1380],{"encoding":597},"2x_1 - x_2 = 1",[572,1382,1384,1444,1499],{"className":1383,"ariaHidden":602},[601],[572,1385,1387,1391,1394,1435,1438,1441],{"className":1386},[606],[572,1388],{"className":1389,"style":1390},[610],"height:0.7944em;vertical-align:-0.15em;",[572,1392,1242],{"className":1393},[615],[572,1395,1397,1400],{"className":1396},[615],[572,1398,754],{"className":1399},[615,616],[572,1401,1403],{"className":1402},[780],[572,1404,1406,1427],{"className":1405},[784,785],[572,1407,1409,1424],{"className":1408},[789],[572,1410,1413],{"className":1411,"style":1412},[793],"height:0.3011em;",[572,1414,1415,1418],{"style":797},[572,1416],{"className":1417,"style":802},[801],[572,1419,1421],{"className":1420},[806,807,808,809],[572,1422,1364],{"className":1423},[615,809],[572,1425,817],{"className":1426},[816],[572,1428,1430],{"className":1429},[789],[572,1431,1433],{"className":1432,"style":824},[793],[572,1434],{},[572,1436],{"className":1437,"style":1267},[696],[572,1439,1367],{"className":1440},[1271],[572,1442],{"className":1443,"style":1267},[696],[572,1445,1447,1450,1490,1493,1496],{"className":1446},[606],[572,1448],{"className":1449,"style":770},[610],[572,1451,1453,1456],{"className":1452},[615],[572,1454,754],{"className":1455},[615,616],[572,1457,1459],{"className":1458},[780],[572,1460,1462,1482],{"className":1461},[784,785],[572,1463,1465,1479],{"className":1464},[789],[572,1466,1468],{"className":1467,"style":1412},[793],[572,1469,1470,1473],{"style":797},[572,1471],{"className":1472,"style":802},[801],[572,1474,1476],{"className":1475},[806,807,808,809],[572,1477,1242],{"className":1478},[615,809],[572,1480,817],{"className":1481},[816],[572,1483,1485],{"className":1484},[789],[572,1486,1488],{"className":1487,"style":824},[793],[572,1489],{},[572,1491],{"className":1492,"style":1148},[696],[572,1494,1072],{"className":1495},[1152],[572,1497],{"className":1498,"style":1148},[696],[572,1500,1502,1505],{"className":1501},[606],[572,1503],{"className":1504,"style":729},[610],[572,1506,1364],{"className":1507},[615]," und ",[572,1510,1512,1546],{"className":1511},[575],[572,1513,1515],{"className":1514},[579],[581,1516,1517],{"xmlns":583},[585,1518,1519,1543],{},[588,1520,1521,1527,1530,1532,1538,1540],{},[750,1522,1523,1525],{},[591,1524,754],{},[715,1526,1364],{},[670,1528,1529],{},"+",[715,1531,1299],{},[750,1533,1534,1536],{},[591,1535,754],{},[715,1537,1242],{},[670,1539,1072],{},[715,1541,1542],{},"11",[595,1544,1545],{"encoding":597},"x_1 + 3x_2 = 11",[572,1547,1549,1605,1663],{"className":1548,"ariaHidden":602},[601],[572,1550,1552,1556,1596,1599,1602],{"className":1551},[606],[572,1553],{"className":1554,"style":1555},[610],"height:0.7333em;vertical-align:-0.15em;",[572,1557,1559,1562],{"className":1558},[615],[572,1560,754],{"className":1561},[615,616],[572,1563,1565],{"className":1564},[780],[572,1566,1568,1588],{"className":1567},[784,785],[572,1569,1571,1585],{"className":1570},[789],[572,1572,1574],{"className":1573,"style":1412},[793],[572,1575,1576,1579],{"style":797},[572,1577],{"className":1578,"style":802},[801],[572,1580,1582],{"className":1581},[806,807,808,809],[572,1583,1364],{"className":1584},[615,809],[572,1586,817],{"className":1587},[816],[572,1589,1591],{"className":1590},[789],[572,1592,1594],{"className":1593,"style":824},[793],[572,1595],{},[572,1597],{"className":1598,"style":1267},[696],[572,1600,1529],{"className":1601},[1271],[572,1603],{"className":1604,"style":1267},[696],[572,1606,1608,1611,1614,1654,1657,1660],{"className":1607},[606],[572,1609],{"className":1610,"style":1390},[610],[572,1612,1299],{"className":1613},[615],[572,1615,1617,1620],{"className":1616},[615],[572,1618,754],{"className":1619},[615,616],[572,1621,1623],{"className":1622},[780],[572,1624,1626,1646],{"className":1625},[784,785],[572,1627,1629,1643],{"className":1628},[789],[572,1630,1632],{"className":1631,"style":1412},[793],[572,1633,1634,1637],{"style":797},[572,1635],{"className":1636,"style":802},[801],[572,1638,1640],{"className":1639},[806,807,808,809],[572,1641,1242],{"className":1642},[615,809],[572,1644,817],{"className":1645},[816],[572,1647,1649],{"className":1648},[789],[572,1650,1652],{"className":1651,"style":824},[793],[572,1653],{},[572,1655],{"className":1656,"style":1148},[696],[572,1658,1072],{"className":1659},[1152],[572,1661],{"className":1662,"style":1148},[696],[572,1664,1666,1669],{"className":1665},[606],[572,1667],{"className":1668,"style":729},[610],[572,1670,1542],{"className":1671},[615],":",[572,1674,1677],{"className":1675},[1676],"katex-display",[572,1678,1680,1874],{"className":1679},[575],[572,1681,1683],{"className":1682},[579],[581,1684,1686],{"xmlns":583,"display":1685},"block",[585,1687,1688,1871],{},[588,1689,1690,1692,1694,1696,1698,1747,1749,1752,1755,1757,1759,1761,1767,1769,1809,1811,1814,1816,1818,1820,1822,1828,1830,1866,1868],{},[591,1691,668],{},[670,1693,672],{},[591,1695,675],{},[670,1697,1072],{},[588,1699,1700,1703,1745],{},[670,1701,1702],{"fence":602},"∣",[1704,1705,1709,1731],"mtable",{"rowspacing":1706,"columnalign":1707,"columnspacing":1708},"0.16em","center 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A = \\begin{vmatrix} 2 & -1 \\\\ 1 & 3 \\end{vmatrix} = 7, \\quad\n\\det A_1 = \\begin{vmatrix} 1 & -1 \\\\ 11 & 3 \\end{vmatrix} = 14, \\quad\n\\det A_2 = \\begin{vmatrix} 2 & 1 \\\\ 1 & 11 \\end{vmatrix} = 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= \\frac{14}{7} = 2, \\qquad x_2 = \\frac{21}{7} = 3",[572,2728,2730,2785,2871,2940,3017],{"className":2729,"ariaHidden":602},[601],[572,2731,2733,2736,2776,2779,2782],{"className":2732},[606],[572,2734],{"className":2735,"style":770},[610],[572,2737,2739,2742],{"className":2738},[615],[572,2740,754],{"className":2741},[615,616],[572,2743,2745],{"className":2744},[780],[572,2746,2748,2768],{"className":2747},[784,785],[572,2749,2751,2765],{"className":2750},[789],[572,2752,2754],{"className":2753,"style":1412},[793],[572,2755,2756,2759],{"style":797},[572,2757],{"className":2758,"style":802},[801],[572,2760,2762],{"className":2761},[806,807,808,809],[572,2763,1364],{"className":2764},[615,809],[572,2766,817],{"className":2767},[816],[572,2769,2771],{"className":2770},[789],[572,2772,2774],{"className":2773,"style":824},[793],[572,2775],{},[572,2777],{"className":2778,"style":1148},[696],[572,2780,1072],{"className":2781},[1152],[572,2783],{"className":2784,"style":1148},[696],[572,2786,2788,2792,2862,2865,2868],{"className":2787},[606],[572,2789],{"className":2790,"style":2791},[610],"height:2.0074em;vertical-align:-0.686em;",[572,2793,2795,2799,2859],{"className":2794},[615],[572,2796],{"className":2797},[1915,2798],"nulldelimiter",[572,2800,2802],{"className":2801},[2691],[572,2803,2805,2850],{"className":2804},[784,785],[572,2806,2808,2847],{"className":2807},[789],[572,2809,2812,2824,2835],{"className":2810,"style":2811},[793],"height:1.3214em;",[572,2813,2815,2818],{"style":2814},"top:-2.314em;",[572,2816],{"className":2817,"style":1016},[801],[572,2819,2821],{"className":2820},[615],[572,2822,1751],{"className":2823},[615],[572,2825,2827,2830],{"style":2826},"top:-3.23em;",[572,2828],{"className":2829,"style":1016},[801],[572,2831],{"className":2832,"style":2834},[2833],"frac-line","border-bottom-width:0.04em;",[572,2836,2838,2841],{"style":2837},"top:-3.677em;",[572,2839],{"className":2840,"style":1016},[801],[572,2842,2844],{"className":2843},[615],[572,2845,1813],{"className":2846},[615],[572,2848,817],{"className":2849},[816],[572,2851,2853],{"className":2852},[789],[572,2854,2857],{"className":2855,"style":2856},[793],"height:0.686em;",[572,2858],{},[572,2860],{"className":2861},[2074,2798],[572,2863],{"className":2864,"style":1148},[696],[572,2866,1072],{"className":2867},[1152],[572,2869],{"className":2870,"style":1148},[696],[572,2872,2874,2878,2881,2884,2888,2891,2931,2934,2937],{"className":2873},[606],[572,2875],{"className":2876,"style":2877},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,2879,1242],{"className":2880},[615],[572,2882,1754],{"className":2883},[2131],[572,2885],{"className":2886,"style":2887},[696],"margin-right:2em;",[572,2889],{"className":2890,"style":697},[696],[572,2892,2894,2897],{"className":2893},[615],[572,2895,754],{"className":2896},[615,616],[572,2898,2900],{"className":2899},[780],[572,2901,2903,2923],{"className":2902},[784,785],[572,2904,2906,2920],{"className":2905},[789],[572,2907,2909],{"className":2908,"style":1412},[793],[572,2910,2911,2914],{"style":797},[572,2912],{"className":2913,"style":802},[801],[572,2915,2917],{"className":2916},[806,807,808,809],[572,2918,1242],{"className":2919},[615,809],[572,2921,817],{"className":2922},[816],[572,2924,2926],{"className":2925},[789],[572,2927,2929],{"className":2928,"style":824},[793],[572,2930],{},[572,2932],{"className":2933,"style":1148},[696],[572,2935,1072],{"className":2936},[1152],[572,2938],{"className":2939,"style":1148},[696],[572,2941,2943,2946,3008,3011,3014],{"className":2942},[606],[572,2944],{"className":2945,"style":2791},[610],[572,2947,2949,2952,3005],{"className":2948},[615],[572,2950],{"className":2951},[1915,2798],[572,2953,2955],{"className":2954},[2691],[572,2956,2958,2997],{"className":2957},[784,785],[572,2959,2961,2994],{"className":2960},[789],[572,2962,2964,2975,2983],{"className":2963,"style":2811},[793],[572,2965,2966,2969],{"style":2814},[572,2967],{"className":2968,"style":1016},[801],[572,2970,2972],{"className":2971},[615],[572,2973,1751],{"className":2974},[615],[572,2976,2977,2980],{"style":2826},[572,2978],{"className":2979,"style":1016},[801],[572,2981],{"className":2982,"style":2834},[2833],[572,2984,2985,2988],{"style":2837},[572,2986],{"className":2987,"style":1016},[801],[572,2989,2991],{"className":2990},[615],[572,2992,1870],{"className":2993},[615],[572,2995,817],{"className":2996},[816],[572,2998,3000],{"className":2999},[789],[572,3001,3003],{"className":3002,"style":2856},[793],[572,3004],{},[572,3006],{"className":3007},[2074,2798],[572,3009],{"className":3010,"style":1148},[696],[572,3012,1072],{"className":3013},[1152],[572,3015],{"className":3016,"style":1148},[696],[572,3018,3020,3023],{"className":3019},[606],[572,3021],{"className":3022,"style":729},[610],[572,3024,1299],{"className":3025},[615],[564,3027,3028,3029,1508,3125,1224],{},"Probe: ",[572,3030,3032,3059],{"className":3031},[575],[572,3033,3035],{"className":3034},[579],[581,3036,3037],{"xmlns":583},[585,3038,3039,3056],{},[588,3040,3041,3043,3046,3048,3050,3052,3054],{},[715,3042,1242],{},[670,3044,3045],{},"⋅",[715,3047,1242],{},[670,3049,1367],{},[715,3051,1299],{},[670,3053,1072],{},[715,3055,1364],{},[595,3057,3058],{"encoding":597},"2 \\cdot 2 - 3 = 1",[572,3060,3062,3080,3098,3116],{"className":3061,"ariaHidden":602},[601],[572,3063,3065,3068,3071,3074,3077],{"className":3064},[606],[572,3066],{"className":3067,"style":729},[610],[572,3069,1242],{"className":3070},[615],[572,3072],{"className":3073,"style":1267},[696],[572,3075,3045],{"className":3076},[1271],[572,3078],{"className":3079,"style":1267},[696],[572,3081,3083,3086,3089,3092,3095],{"className":3082},[606],[572,3084],{"className":3085,"style":1260},[610],[572,3087,1242],{"className":3088},[615],[572,3090],{"className":3091,"style":1267},[696],[572,3093,1367],{"className":3094},[1271],[572,3096],{"className":3097,"style":1267},[696],[572,3099,3101,3104,3107,3110,3113],{"className":3100},[606],[572,3102],{"className":3103,"style":729},[610],[572,3105,1299],{"className":3106},[615],[572,3108],{"className":3109,"style":1148},[696],[572,3111,1072],{"className":3112},[1152],[572,3114],{"className":3115,"style":1148},[696],[572,3117,3119,3122],{"className":3118},[606],[572,3120],{"className":3121,"style":729},[610],[572,3123,1364],{"className":3124},[615],[572,3126,3128,3154],{"className":3127},[575],[572,3129,3131],{"className":3130},[579],[581,3132,3133],{"xmlns":583},[585,3134,3135,3151],{},[588,3136,3137,3139,3141,3143,3145,3147,3149],{},[715,3138,1242],{},[670,3140,1529],{},[715,3142,1299],{},[670,3144,3045],{},[715,3146,1299],{},[670,3148,1072],{},[715,3150,1542],{},[595,3152,3153],{"encoding":597},"2 + 3 \\cdot 3 = 11",[572,3155,3157,3175,3193,3211],{"className":3156,"ariaHidden":602},[601],[572,3158,3160,3163,3166,3169,3172],{"className":3159},[606],[572,3161],{"className":3162,"style":1260},[610],[572,3164,1242],{"className":3165},[615],[572,3167],{"className":3168,"style":1267},[696],[572,3170,1529],{"className":3171},[1271],[572,3173],{"className":3174,"style":1267},[696],[572,3176,3178,3181,3184,3187,3190],{"className":3177},[606],[572,3179],{"className":3180,"style":729},[610],[572,3182,1299],{"className":3183},[615],[572,3185],{"className":3186,"style":1267},[696],[572,3188,3045],{"className":3189},[1271],[572,3191],{"className":3192,"style":1267},[696],[572,3194,3196,3199,3202,3205,3208],{"className":3195},[606],[572,3197],{"className":3198,"style":729},[610],[572,3200,1299],{"className":3201},[615],[572,3203],{"className":3204,"style":1148},[696],[572,3206,1072],{"className":3207},[1152],[572,3209],{"className":3210,"style":1148},[696],[572,3212,3214,3217],{"className":3213},[606],[572,3215],{"className":3216,"style":729},[610],[572,3218,1542],{"className":3219},[615],[564,3221,3222,3223,3273,3274,3376,3377,3376,3477,3577],{},"Ein ",[572,3224,3226,3243],{"className":3225},[575],[572,3227,3229],{"className":3228},[579],[581,3230,3231],{"xmlns":583},[585,3232,3233,3241],{},[588,3234,3235,3237,3239],{},[715,3236,1299],{},[670,3238,1245],{},[715,3240,1299],{},[595,3242,1306],{"encoding":597},[572,3244,3246,3264],{"className":3245,"ariaHidden":602},[601],[572,3247,3249,3252,3255,3258,3261],{"className":3248},[606],[572,3250],{"className":3251,"style":1260},[610],[572,3253,1299],{"className":3254},[615],[572,3256],{"className":3257,"style":1267},[696],[572,3259,1245],{"className":3260},[1271],[572,3262],{"className":3263,"style":1267},[696],[572,3265,3267,3270],{"className":3266},[606],[572,3268],{"className":3269,"style":729},[610],[572,3271,1299],{"className":3272},[615],"-System: ",[572,3275,3277,3306],{"className":3276},[575],[572,3278,3280],{"className":3279},[579],[581,3281,3282],{"xmlns":583},[585,3283,3284,3303],{},[588,3285,3286,3288,3290,3293,3295,3298,3300],{},[591,3287,754],{},[670,3289,1529],{},[591,3291,3292],{},"y",[670,3294,1529],{},[591,3296,3297],{},"z",[670,3299,1072],{},[715,3301,3302],{},"6",[595,3304,3305],{"encoding":597},"x + y + z = 6",[572,3307,3309,3328,3348,3367],{"className":3308,"ariaHidden":602},[601],[572,3310,3312,3316,3319,3322,3325],{"className":3311},[606],[572,3313],{"className":3314,"style":3315},[610],"height:0.6667em;vertical-align:-0.0833em;",[572,3317,754],{"className":3318},[615,616],[572,3320],{"className":3321,"style":1267},[696],[572,3323,1529],{"className":3324},[1271],[572,3326],{"className":3327,"style":1267},[696],[572,3329,3331,3335,3339,3342,3345],{"className":3330},[606],[572,3332],{"className":3333,"style":3334},[610],"height:0.7778em;vertical-align:-0.1944em;",[572,3336,3292],{"className":3337,"style":3338},[615,616],"margin-right:0.0359em;",[572,3340],{"className":3341,"style":1267},[696],[572,3343,1529],{"className":3344},[1271],[572,3346],{"className":3347,"style":1267},[696],[572,3349,3351,3354,3358,3361,3364],{"className":3350},[606],[572,3352],{"className":3353,"style":611},[610],[572,3355,3297],{"className":3356,"style":3357},[615,616],"margin-right:0.044em;",[572,3359],{"className":3360,"style":1148},[696],[572,3362,1072],{"className":3363},[1152],[572,3365],{"className":3366,"style":1148},[696],[572,3368,3370,3373],{"className":3369},[606],[572,3371],{"className":3372,"style":729},[610],[572,3374,3302],{"className":3375},[615],", ",[572,3378,3380,3408],{"className":3379},[575],[572,3381,3383],{"className":3382},[579],[581,3384,3385],{"xmlns":583},[585,3386,3387,3405],{},[588,3388,3389,3391,3393,3395,3397,3399,3401,3403],{},[715,3390,1242],{},[591,3392,754],{},[670,3394,1367],{},[591,3396,3292],{},[670,3398,1529],{},[591,3400,3297],{},[670,3402,1072],{},[715,3404,1299],{},[595,3406,3407],{"encoding":597},"2x - y + z = 3",[572,3409,3411,3432,3450,3468],{"className":3410,"ariaHidden":602},[601],[572,3412,3414,3417,3420,3423,3426,3429],{"className":3413},[606],[572,3415],{"className":3416,"style":1260},[610],[572,3418,1242],{"className":3419},[615],[572,3421,754],{"className":3422},[615,616],[572,3424],{"className":3425,"style":1267},[696],[572,3427,1367],{"className":3428},[1271],[572,3430],{"className":3431,"style":1267},[696],[572,3433,3435,3438,3441,3444,3447],{"className":3434},[606],[572,3436],{"className":3437,"style":3334},[610],[572,3439,3292],{"className":3440,"style":3338},[615,616],[572,3442],{"className":3443,"style":1267},[696],[572,3445,1529],{"className":3446},[1271],[572,3448],{"className":3449,"style":1267},[696],[572,3451,3453,3456,3459,3462,3465],{"className":3452},[606],[572,3454],{"className":3455,"style":611},[610],[572,3457,3297],{"className":3458,"style":3357},[615,616],[572,3460],{"className":3461,"style":1148},[696],[572,3463,1072],{"className":3464},[1152],[572,3466],{"className":3467,"style":1148},[696],[572,3469,3471,3474],{"className":3470},[606],[572,3472],{"className":3473,"style":729},[610],[572,3475,1299],{"className":3476},[615],[572,3478,3480,3508],{"className":3479},[575],[572,3481,3483],{"className":3482},[579],[581,3484,3485],{"xmlns":583},[585,3486,3487,3505],{},[588,3488,3489,3491,3493,3495,3497,3499,3501,3503],{},[591,3490,754],{},[670,3492,1529],{},[715,3494,1242],{},[591,3496,3292],{},[670,3498,1367],{},[591,3500,3297],{},[670,3502,1072],{},[715,3504,1242],{},[595,3506,3507],{"encoding":597},"x + 2y - z = 2",[572,3509,3511,3529,3550,3568],{"className":3510,"ariaHidden":602},[601],[572,3512,3514,3517,3520,3523,3526],{"className":3513},[606],[572,3515],{"className":3516,"style":3315},[610],[572,3518,754],{"className":3519},[615,616],[572,3521],{"className":3522,"style":1267},[696],[572,3524,1529],{"className":3525},[1271],[572,3527],{"className":3528,"style":1267},[696],[572,3530,3532,3535,3538,3541,3544,3547],{"className":3531},[606],[572,3533],{"className":3534,"style":2877},[610],[572,3536,1242],{"className":3537},[615],[572,3539,3292],{"className":3540,"style":3338},[615,616],[572,3542],{"className":3543,"style":1267},[696],[572,3545,1367],{"className":3546},[1271],[572,3548],{"className":3549,"style":1267},[696],[572,3551,3553,3556,3559,3562,3565],{"className":3552},[606],[572,3554],{"className":3555,"style":611},[610],[572,3557,3297],{"className":3558,"style":3357},[615,616],[572,3560],{"className":3561,"style":1148},[696],[572,3563,1072],{"className":3564},[1152],[572,3566],{"className":3567,"style":1148},[696],[572,3569,3571,3574],{"className":3570},[606],[572,3572],{"className":3573,"style":729},[610],[572,3575,1242],{"className":3576},[615],". Mit der Regel von Sarrus:",[572,3579,3581],{"className":3580},[1676],[572,3582,3584,3781],{"className":3583},[575],[572,3585,3587],{"className":3586},[579],[581,3588,3589],{"xmlns":583,"display":1685},[585,3590,3591,3778],{},[588,3592,3593,3595,3597,3599,3601,3678,3680,3682,3684,3686,3688,3690,3696,3698,3774,3776],{},[591,3594,668],{},[670,3596,672],{},[591,3598,675],{},[670,3600,1072],{},[588,3602,3603,3605,3676],{},[670,3604,1702],{"fence":602},[1704,3606,3608,3628,3652],{"rowspacing":1706,"columnalign":3607,"columnspacing":1708},"center center center",[1710,3609,3610,3616,3622],{},[1713,3611,3612],{},[1716,3613,3614],{"scriptlevel":717,"displaystyle":1718},[715,3615,1364],{},[1713,3617,3618],{},[1716,3619,3620],{"scriptlevel":717,"displaystyle":1718},[715,3621,1364],{},[1713,3623,3624],{},[1716,3625,3626],{"scriptlevel":717,"displaystyle":1718},[715,3627,1364],{},[1710,3629,3630,3636,3646],{},[1713,3631,3632],{},[1716,3633,3634],{"scriptlevel":717,"displaystyle":1718},[715,3635,1242],{},[1713,3637,3638],{},[1716,3639,3640],{"scriptlevel":717,"displaystyle":1718},[588,3641,3642,3644],{},[670,3643,1367],{},[715,3645,1364],{},[1713,3647,3648],{},[1716,3649,3650],{"scriptlevel":717,"displaystyle":1718},[715,3651,1364],{},[1710,3653,3654,3660,3666],{},[1713,3655,3656],{},[1716,3657,3658],{"scriptlevel":717,"displaystyle":1718},[715,3659,1364],{},[1713,3661,3662],{},[1716,3663,3664],{"scriptlevel":717,"displaystyle":1718},[715,3665,1242],{},[1713,3667,3668],{},[1716,3669,3670],{"scriptlevel":717,"displaystyle":1718},[588,3671,3672,3674],{},[670,3673,1367],{},[715,3675,1364],{},[670,3677,1702],{"fence":602},[670,3679,1072],{},[715,3681,1751],{},[670,3683,1754],{"separator":602},[696,3685],{"width":1708},[591,3687,668],{},[670,3689,672],{},[750,3691,3692,3694],{},[591,3693,675],{},[715,3695,1364],{},[670,3697,1072],{},[588,3699,3700,3702,3772],{},[670,3701,1702],{"fence":602},[1704,3703,3704,3724,3748],{"rowspacing":1706,"columnalign":3607,"columnspacing":1708},[1710,3705,3706,3712,3718],{},[1713,3707,3708],{},[1716,3709,3710],{"scriptlevel":717,"displaystyle":1718},[715,3711,3302],{},[1713,3713,3714],{},[1716,3715,3716],{"scriptlevel":717,"displaystyle":1718},[715,3717,1364],{},[1713,3719,3720],{},[1716,3721,3722],{"scriptlevel":717,"displaystyle":1718},[715,3723,1364],{},[1710,3725,3726,3732,3742],{},[1713,3727,3728],{},[1716,3729,3730],{"scriptlevel":717,"displaystyle":1718},[715,3731,1299],{},[1713,3733,3734],{},[1716,3735,3736],{"scriptlevel":717,"displaystyle":1718},[588,3737,3738,3740],{},[670,3739,1367],{},[715,3741,1364],{},[1713,3743,3744],{},[1716,3745,3746],{"scriptlevel":717,"displaystyle":1718},[715,3747,1364],{},[1710,3749,3750,3756,3762],{},[1713,3751,3752],{},[1716,3753,3754],{"scriptlevel":717,"displaystyle":1718},[715,3755,1242],{},[1713,3757,3758],{},[1716,3759,3760],{"scriptlevel":717,"displaystyle":1718},[715,3761,1242],{},[1713,3763,3764],{},[1716,3765,3766],{"scriptlevel":717,"displaystyle":1718},[588,3767,3768,3770],{},[670,3769,1367],{},[715,3771,1364],{},[670,3773,1702],{"fence":602},[670,3775,1072],{},[715,3777,1751],{},[595,3779,3780],{"encoding":597},"\\det A = \\begin{vmatrix} 1 & 1 & 1 \\\\ 2 & -1 & 1 \\\\ 1 & 2 & -1 \\end{vmatrix} = 7, \\quad\n\\det A_1 = \\begin{vmatrix} 6 & 1 & 1 \\\\ 3 & -1 & 1 \\\\ 2 & 2 & -1 \\end{vmatrix} = 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3",[572,5505,5507,5525],{"className":5506,"ariaHidden":602},[601],[572,5508,5510,5513,5516,5519,5522],{"className":5509},[606],[572,5511],{"className":5512,"style":611},[610],[572,5514,3297],{"className":5515,"style":3357},[615,616],[572,5517],{"className":5518,"style":1148},[696],[572,5520,1072],{"className":5521},[1152],[572,5523],{"className":5524,"style":1148},[696],[572,5526,5528,5531],{"className":5527},[606],[572,5529],{"className":5530,"style":729},[610],[572,5532,1299],{"className":5533},[615],[559,5535,5537],{"id":5536},"typische-fehler","Typische Fehler",[5539,5540,5541,5613,5678,5780],"ul",{},[651,5542,5543,5544,5547,5548,5612],{},"Eine ",[568,5545,5546],{},"Zeile"," statt einer Spalte durch ",[572,5549,5551,5568],{"className":5550},[575],[572,5552,5554],{"className":5553},[579],[581,5555,5556],{"xmlns":583},[585,5557,5558,5566],{},[588,5559,5560],{},[976,5561,5562,5564],{"accent":602},[591,5563,980],{},[670,5565,983],{},[595,5567,986],{"encoding":597},[572,5569,5571],{"className":5570,"ariaHidden":602},[601],[572,5572,5574,5577],{"className":5573},[606],[572,5575],{"className":5576,"style":996},[610],[572,5578,5580],{"className":5579},[615,1000],[572,5581,5583],{"className":5582},[784],[572,5584,5586],{"className":5585},[789],[572,5587,5589,5597],{"className":5588,"style":996},[793],[572,5590,5591,5594],{"style":1012},[572,5592],{"className":5593,"style":1016},[801],[572,5595,980],{"className":5596},[615,616],[572,5598,5599,5602],{"style":1022},[572,5600],{"className":5601,"style":1016},[801],[572,5603,5605],{"className":5604,"style":1030},[1029],[572,5606,5608],{"className":5607,"style":1035},[1034],[1037,5609,5610],{"xmlns":1039,"width":1040,"height":1041,"style":1042,"viewBox":1043,"preserveAspectRatio":1044},[1046,5611],{"d":1048}," ersetzen.",[651,5614,5615,5616,5677],{},"Die Regel bei ",[572,5617,5619,5641],{"className":5618},[575],[572,5620,5622],{"className":5621},[579],[581,5623,5624],{"xmlns":583},[585,5625,5626,5638],{},[588,5627,5628,5630,5632,5634,5636],{},[591,5629,668],{},[670,5631,672],{},[591,5633,675],{},[670,5635,1072],{},[715,5637,717],{},[595,5639,5640],{"encoding":597},"\\det A = 0",[572,5642,5644,5668],{"className":5643,"ariaHidden":602},[601],[572,5645,5647,5650,5653,5656,5659,5662,5665],{"className":5646},[606],[572,5648],{"className":5649,"style":688},[610],[572,5651,668],{"className":5652},[692],[572,5654],{"className":5655,"style":697},[696],[572,5657,675],{"className":5658},[615,616],[572,5660],{"className":5661,"style":1148},[696],[572,5663,1072],{"className":5664},[1152],[572,5666],{"className":5667,"style":1148},[696],[572,5669,5671,5674],{"className":5670},[606],[572,5672],{"className":5673,"style":729},[610],[572,5675,717],{"className":5676},[615]," anwenden. Dann ist das System nicht eindeutig lösbar.",[651,5679,5680,5681,5750,5751,5779],{},"Bei ",[572,5682,5684,5701],{"className":5683},[575],[572,5685,5687],{"className":5686},[579],[581,5688,5689],{"xmlns":583},[585,5690,5691,5699],{},[588,5692,5693],{},[750,5694,5695,5697],{},[591,5696,675],{},[591,5698,757],{},[595,5700,848],{"encoding":597},[572,5702,5704],{"className":5703,"ariaHidden":602},[601],[572,5705,5707,5710],{"className":5706},[606],[572,5708],{"className":5709,"style":858},[610],[572,5711,5713,5716],{"className":5712},[615],[572,5714,675],{"className":5715},[615,616],[572,5717,5719],{"className":5718},[780],[572,5720,5722,5742],{"className":5721},[784,785],[572,5723,5725,5739],{"className":5724},[789],[572,5726,5728],{"className":5727,"style":794},[793],[572,5729,5730,5733],{"style":797},[572,5731],{"className":5732,"style":802},[801],[572,5734,5736],{"className":5735},[806,807,808,809],[572,5737,757],{"className":5738},[615,616,809],[572,5740,817],{"className":5741},[816],[572,5743,5745],{"className":5744},[789],[572,5746,5748],{"className":5747,"style":824},[793],[572,5749],{}," die übrigen Spalten verändern. Nur die ",[572,5752,5754,5767],{"className":5753},[575],[572,5755,5757],{"className":5756},[579],[581,5758,5759],{"xmlns":583},[585,5760,5761,5765],{},[588,5762,5763],{},[591,5764,757],{},[595,5766,757],{"encoding":597},[572,5768,5770],{"className":5769,"ariaHidden":602},[601],[572,5771,5773,5776],{"className":5772},[606],[572,5774],{"className":5775,"style":957},[610],[572,5777,757],{"className":5778},[615,616],"-te Spalte wird ausgetauscht, alle anderen bleiben, wie sie sind.",[651,5781,5782,5783,1224],{},"Gleichungen nicht vorher ordnen: Die Unbekannten müssen in jeder Gleichung in derselben Reihenfolge stehen, fehlende Unbekannte bekommen den Koeffizienten ",[572,5784,5786,5799],{"className":5785},[575],[572,5787,5789],{"className":5788},[579],[581,5790,5791],{"xmlns":583},[585,5792,5793,5797],{},[588,5794,5795],{},[715,5796,717],{},[595,5798,717],{"encoding":597},[572,5800,5802],{"className":5801,"ariaHidden":602},[601],[572,5803,5805,5808],{"className":5804},[606],[572,5806],{"className":5807,"style":729},[610],[572,5809,717],{"className":5810},[615],{"title":5812,"searchDepth":5813,"depth":5813,"links":5814},"",2,[5815,5816,5817],{"id":561,"depth":5813,"text":562},{"id":1340,"depth":5813,"text":1341},{"id":5536,"depth":5813,"text":5537},[5819,5822,5825,5827,5829,5831,5833,5835,5837,5839,5841,5843,5845,5847],{"lhs":5820,"rhs":5821},"a11*(b1*a22 - a12*b2)\u002F(a11*a22 - a12*a21) + a12*(a11*b2 - b1*a21)\u002F(a11*a22 - a12*a21)","b1",{"lhs":5823,"rhs":5824},"a21*(b1*a22 - a12*b2)\u002F(a11*a22 - a12*a21) + a22*(a11*b2 - b1*a21)\u002F(a11*a22 - a12*a21)","b2",{"lhs":5826,"rhs":1751},"det([[2, -1], [1, 3]])",{"lhs":5828,"rhs":1813},"det([[1, -1], [11, 3]])",{"lhs":5830,"rhs":1870},"det([[2, 1], [1, 11]])",{"lhs":5832,"rhs":1364},"2*2 - 3",{"lhs":5834,"rhs":1542},"2 + 3*3",{"lhs":5836,"rhs":1751},"det([[1, 1, 1], [2, -1, 1], [1, 2, -1]])",{"lhs":5838,"rhs":1751},"det([[6, 1, 1], [3, -1, 1], [2, 2, -1]])",{"lhs":5840,"rhs":1813},"det([[1, 6, 1], [2, 3, 1], [1, 2, -1]])",{"lhs":5842,"rhs":1870},"det([[1, 1, 6], [2, -1, 3], [1, 2, 2]])",{"lhs":5844,"rhs":3302},"1 + 2 + 3",{"lhs":5846,"rhs":1299},"2*1 - 2 + 3",{"lhs":5848,"rhs":1242},"1 + 2*2 - 3","A\\vec{x} = \\vec{b},\\ A \\in \\mathbb{R}^{n \\times n},\\ \\det A \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\\vec{x} = \\vec{b},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1719em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{n \\times n},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\det A \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","cramers-rule","x_i = \\frac{\\det A_i}{\\det A}","\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>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i = \\frac{\\det A_i}{\\det A}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\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:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" 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