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löst die ",[569,1079,1080],{},"Normalgleichungen"," ",[574,1083,1085,1126],{"className":1084},[577],[574,1086,1088],{"className":1087},[581],[583,1089,1090],{"xmlns":585},[587,1091,1092,1123],{},[590,1093,1094,1101,1103,1109,1111,1117],{},[852,1095,1096,1098],{},[593,1097,595],{},[593,1099,1100],{},"T",[593,1102,595],{},[597,1104,1105,1107],{"accent":599},[593,1106,602],{},[604,1108,606],{},[604,1110,609],{},[852,1112,1113,1115],{},[593,1114,595],{},[593,1116,1100],{},[597,1118,1119,1121],{"accent":599},[593,1120,614],{},[604,1122,606],{},[618,1124,1125],{"encoding":620},"A^T A \\vec x = A^T \\vec b",[574,1127,1129,1213],{"className":1128,"ariaHidden":599},[625],[574,1130,1132,1136,1166,1169,1204,1207,1210],{"className":1131},[629],[574,1133],{"className":1134,"style":1135},[633],"height:0.8413em;",[574,1137,1139,1142],{"className":1138},[638],[574,1140,595],{"className":1141},[638,639],[574,1143,1145],{"className":1144},[978],[574,1146,1148],{"className":1147},[647],[574,1149,1151],{"className":1150},[651],[574,1152,1154],{"className":1153,"style":1135},[655],[574,1155,1156,1159],{"style":991},[574,1157],{"className":1158,"style":995},[662],[574,1160,1162],{"className":1161},[999,1000,1001,1002],[574,1163,1100],{"className":1164,"style":1165},[638,639,1002],"margin-right:0.1389em;",[574,1167,595],{"className":1168},[638,639],[574,1170,1172],{"className":1171},[638,643],[574,1173,1175],{"className":1174},[647],[574,1176,1178],{"className":1177},[651],[574,1179,1181,1189],{"className":1180,"style":634},[655],[574,1182,1183,1186],{"style":658},[574,1184],{"className":1185,"style":663},[662],[574,1187,602],{"className":1188},[638,639],[574,1190,1191,1194],{"style":658},[574,1192],{"className":1193,"style":663},[662],[574,1195,1197],{"className":1196,"style":676},[675],[574,1198,1200],{"className":1199,"style":681},[680],[683,1201,1202],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1203],{"d":694},[574,1205],{"className":1206,"style":699},[698],[574,1208,609],{"className":1209},[703],[574,1211],{"className":1212,"style":699},[698],[574,1214,1216,1219,1248],{"className":1215},[629],[574,1217],{"className":1218,"style":713},[633],[574,1220,1222,1225],{"className":1221},[638],[574,1223,595],{"className":1224},[638,639],[574,1226,1228],{"className":1227},[978],[574,1229,1231],{"className":1230},[647],[574,1232,1234],{"className":1233},[651],[574,1235,1237],{"className":1236,"style":1135},[655],[574,1238,1239,1242],{"style":991},[574,1240],{"className":1241,"style":995},[662],[574,1243,1245],{"className":1244},[999,1000,1001,1002],[574,1246,1100],{"className":1247,"style":1165},[638,639,1002],[574,1249,1251],{"className":1250},[638,643],[574,1252,1254],{"className":1253},[647],[574,1255,1257],{"className":1256},[651],[574,1258,1260,1268],{"className":1259,"style":713},[655],[574,1261,1262,1265],{"style":658},[574,1263],{"className":1264,"style":663},[662],[574,1266,614],{"className":1267},[638,639],[574,1269,1270,1273],{"style":736},[574,1271],{"className":1272,"style":663},[662],[574,1274,1276],{"className":1275,"style":743},[675],[574,1277,1279],{"className":1278,"style":681},[680],[683,1280,1281],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1282],{"d":694},". Der Grund ist geometrisch: ",[574,1285,1287,1307],{"className":1286},[577],[574,1288,1290],{"className":1289},[581],[583,1291,1292],{"xmlns":585},[587,1293,1294,1304],{},[590,1295,1296,1298],{},[593,1297,595],{},[597,1299,1300,1302],{"accent":599},[593,1301,602],{},[604,1303,606],{},[618,1305,1306],{"encoding":620},"A\\vec x",[574,1308,1310],{"className":1309,"ariaHidden":599},[625],[574,1311,1313,1316,1319],{"className":1312},[629],[574,1314],{"className":1315,"style":634},[633],[574,1317,595],{"className":1318},[638,639],[574,1320,1322],{"className":1321},[638,643],[574,1323,1325],{"className":1324},[647],[574,1326,1328],{"className":1327},[651],[574,1329,1331,1339],{"className":1330,"style":634},[655],[574,1332,1333,1336],{"style":658},[574,1334],{"className":1335,"style":663},[662],[574,1337,602],{"className":1338},[638,639],[574,1340,1341,1344],{"style":658},[574,1342],{"className":1343,"style":663},[662],[574,1345,1347],{"className":1346,"style":676},[675],[574,1348,1350],{"className":1349,"style":681},[680],[683,1351,1352],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1353],{"d":694}," ist der Punkt im Spaltenraum von ",[574,1356,1358,1371],{"className":1357},[577],[574,1359,1361],{"className":1360},[581],[583,1362,1363],{"xmlns":585},[587,1364,1365,1369],{},[590,1366,1367],{},[593,1368,595],{},[618,1370,595],{"encoding":620},[574,1372,1374],{"className":1373,"ariaHidden":599},[625],[574,1375,1377,1381],{"className":1376},[629],[574,1378],{"className":1379,"style":1380},[633],"height:0.6833em;",[574,1382,595],{"className":1383},[638,639],", der ",[574,1386,1388,1406],{"className":1387},[577],[574,1389,1391],{"className":1390},[581],[583,1392,1393],{"xmlns":585},[587,1394,1395,1403],{},[590,1396,1397],{},[597,1398,1399,1401],{"accent":599},[593,1400,614],{},[604,1402,606],{},[618,1404,1405],{"encoding":620},"\\vec b",[574,1407,1409],{"className":1408,"ariaHidden":599},[625],[574,1410,1412,1415],{"className":1411},[629],[574,1413],{"className":1414,"style":713},[633],[574,1416,1418],{"className":1417},[638,643],[574,1419,1421],{"className":1420},[647],[574,1422,1424],{"className":1423},[651],[574,1425,1427,1435],{"className":1426,"style":713},[655],[574,1428,1429,1432],{"style":658},[574,1430],{"className":1431,"style":663},[662],[574,1433,614],{"className":1434},[638,639],[574,1436,1437,1440],{"style":736},[574,1438],{"className":1439,"style":663},[662],[574,1441,1443],{"className":1442,"style":743},[675],[574,1444,1446],{"className":1445,"style":681},[680],[683,1447,1448],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1449],{"d":694}," am nächsten liegt, also die orthogonale Projektion von ",[574,1452,1454,1471],{"className":1453},[577],[574,1455,1457],{"className":1456},[581],[583,1458,1459],{"xmlns":585},[587,1460,1461,1469],{},[590,1462,1463],{},[597,1464,1465,1467],{"accent":599},[593,1466,614],{},[604,1468,606],{},[618,1470,1405],{"encoding":620},[574,1472,1474],{"className":1473,"ariaHidden":599},[625],[574,1475,1477,1480],{"className":1476},[629],[574,1478],{"className":1479,"style":713},[633],[574,1481,1483],{"className":1482},[638,643],[574,1484,1486],{"className":1485},[647],[574,1487,1489],{"className":1488},[651],[574,1490,1492,1500],{"className":1491,"style":713},[655],[574,1493,1494,1497],{"style":658},[574,1495],{"className":1496,"style":663},[662],[574,1498,614],{"className":1499},[638,639],[574,1501,1502,1505],{"style":736},[574,1503],{"className":1504,"style":663},[662],[574,1506,1508],{"className":1507,"style":743},[675],[574,1509,1511],{"className":1510,"style":681},[680],[683,1512,1513],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1514],{"d":694},". Das ",[569,1517,1518],{},"Residuum",[574,1520,1522,1559],{"className":1521},[577],[574,1523,1525],{"className":1524},[581],[583,1526,1527],{"xmlns":585},[587,1528,1529,1556],{},[590,1530,1531,1538,1540,1546,1548,1550],{},[597,1532,1533,1536],{"accent":599},[593,1534,1535],{},"r",[604,1537,606],{},[604,1539,609],{},[597,1541,1542,1544],{"accent":599},[593,1543,614],{},[604,1545,606],{},[604,1547,844],{},[593,1549,595],{},[597,1551,1552,1554],{"accent":599},[593,1553,602],{},[604,1555,606],{},[618,1557,1558],{"encoding":620},"\\vec r = \\vec b - A\\vec x",[574,1560,1562,1614,1665],{"className":1561,"ariaHidden":599},[625],[574,1563,1565,1568,1605,1608,1611],{"className":1564},[629],[574,1566],{"className":1567,"style":634},[633],[574,1569,1571],{"className":1570},[638,643],[574,1572,1574],{"className":1573},[647],[574,1575,1577],{"className":1576},[651],[574,1578,1580,1589],{"className":1579,"style":634},[655],[574,1581,1582,1585],{"style":658},[574,1583],{"className":1584,"style":663},[662],[574,1586,1535],{"className":1587,"style":1588},[638,639],"margin-right:0.0278em;",[574,1590,1591,1594],{"style":658},[574,1592],{"className":1593,"style":663},[662],[574,1595,1598],{"className":1596,"style":1597},[675],"left:-0.1799em;",[574,1599,1601],{"className":1600,"style":681},[680],[683,1602,1603],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1604],{"d":694},[574,1606],{"className":1607,"style":699},[698],[574,1609,609],{"className":1610},[703],[574,1612],{"className":1613,"style":699},[698],[574,1615,1617,1621,1656,1659,1662],{"className":1616},[629],[574,1618],{"className":1619,"style":1620},[633],"height:1.0608em;vertical-align:-0.0833em;",[574,1622,1624],{"className":1623},[638,643],[574,1625,1627],{"className":1626},[647],[574,1628,1630],{"className":1629},[651],[574,1631,1633,1641],{"className":1632,"style":713},[655],[574,1634,1635,1638],{"style":658},[574,1636],{"className":1637,"style":663},[662],[574,1639,614],{"className":1640},[638,639],[574,1642,1643,1646],{"style":736},[574,1644],{"className":1645,"style":663},[662],[574,1647,1649],{"className":1648,"style":743},[675],[574,1650,1652],{"className":1651,"style":681},[680],[683,1653,1654],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1655],{"d":694},[574,1657],{"className":1658,"style":918},[698],[574,1660,844],{"className":1661},[922],[574,1663],{"className":1664,"style":918},[698],[574,1666,1668,1671,1674],{"className":1667},[629],[574,1669],{"className":1670,"style":634},[633],[574,1672,595],{"className":1673},[638,639],[574,1675,1677],{"className":1676},[638,643],[574,1678,1680],{"className":1679},[647],[574,1681,1683],{"className":1682},[651],[574,1684,1686,1694],{"className":1685,"style":634},[655],[574,1687,1688,1691],{"style":658},[574,1689],{"className":1690,"style":663},[662],[574,1692,602],{"className":1693},[638,639],[574,1695,1696,1699],{"style":658},[574,1697],{"className":1698,"style":663},[662],[574,1700,1702],{"className":1701,"style":676},[675],[574,1703,1705],{"className":1704,"style":681},[680],[683,1706,1707],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1708],{"d":694}," steht deshalb senkrecht auf allen Spalten von ",[574,1711,1713,1726],{"className":1712},[577],[574,1714,1716],{"className":1715},[581],[583,1717,1718],{"xmlns":585},[587,1719,1720,1724],{},[590,1721,1722],{},[593,1723,595],{},[618,1725,595],{"encoding":620},[574,1727,1729],{"className":1728,"ariaHidden":599},[625],[574,1730,1732,1735],{"className":1731},[629],[574,1733],{"className":1734,"style":1380},[633],[574,1736,595],{"className":1737},[638,639],", das heißt ",[574,1740,1742,1775],{"className":1741},[577],[574,1743,1745],{"className":1744},[581],[583,1746,1747],{"xmlns":585},[587,1748,1749,1772],{},[590,1750,1751,1757,1763,1765],{},[852,1752,1753,1755],{},[593,1754,595],{},[593,1756,1100],{},[597,1758,1759,1761],{"accent":599},[593,1760,1535],{},[604,1762,606],{},[604,1764,609],{},[597,1766,1767,1770],{"accent":599},[857,1768,1769],{},"0",[604,1771,606],{},[618,1773,1774],{"encoding":620},"A^T \\vec r = \\vec 0",[574,1776,1778,1857],{"className":1777,"ariaHidden":599},[625],[574,1779,1781,1784,1813,1848,1851,1854],{"className":1780},[629],[574,1782],{"className":1783,"style":1135},[633],[574,1785,1787,1790],{"className":1786},[638],[574,1788,595],{"className":1789},[638,639],[574,1791,1793],{"className":1792},[978],[574,1794,1796],{"className":1795},[647],[574,1797,1799],{"className":1798},[651],[574,1800,1802],{"className":1801,"style":1135},[655],[574,1803,1804,1807],{"style":991},[574,1805],{"className":1806,"style":995},[662],[574,1808,1810],{"className":1809},[999,1000,1001,1002],[574,1811,1100],{"className":1812,"style":1165},[638,639,1002],[574,1814,1816],{"className":1815},[638,643],[574,1817,1819],{"className":1818},[647],[574,1820,1822],{"className":1821},[651],[574,1823,1825,1833],{"className":1824,"style":634},[655],[574,1826,1827,1830],{"style":658},[574,1828],{"className":1829,"style":663},[662],[574,1831,1535],{"className":1832,"style":1588},[638,639],[574,1834,1835,1838],{"style":658},[574,1836],{"className":1837,"style":663},[662],[574,1839,1841],{"className":1840,"style":1597},[675],[574,1842,1844],{"className":1843,"style":681},[680],[683,1845,1846],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1847],{"d":694},[574,1849],{"className":1850,"style":699},[698],[574,1852,609],{"className":1853},[703],[574,1855],{"className":1856,"style":699},[698],[574,1858,1860,1864],{"className":1859},[629],[574,1861],{"className":1862,"style":1863},[633],"height:0.9274em;",[574,1865,1867],{"className":1866},[638,643],[574,1868,1870],{"className":1869},[647],[574,1871,1873],{"className":1872},[651],[574,1874,1876,1884],{"className":1875,"style":1863},[655],[574,1877,1878,1881],{"style":658},[574,1879],{"className":1880,"style":663},[662],[574,1882,1769],{"className":1883},[638],[574,1885,1887,1890],{"style":1886},"top:-3.2134em;",[574,1888],{"className":1889,"style":663},[662],[574,1891,1893],{"className":1892,"style":743},[675],[574,1894,1896],{"className":1895,"style":681},[680],[683,1897,1898],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,1899],{"d":694},". Umgestellt sind das die Normalgleichungen.",[565,1902,1903],{},"Lösbarkeit:",[1905,1906,1907,1915],"ul",{},[1908,1909,1910,1911,1914],"li",{},"Die Normalgleichungen sind ",[569,1912,1913],{},"immer"," lösbar.",[1908,1916,1917,1981,1982,2010,2011,2092,2093,1009],{},[574,1918,1920,1940],{"className":1919},[577],[574,1921,1923],{"className":1922},[581],[583,1924,1925],{"xmlns":585},[587,1926,1927,1937],{},[590,1928,1929,1935],{},[852,1930,1931,1933],{},[593,1932,595],{},[593,1934,1100],{},[593,1936,595],{},[618,1938,1939],{"encoding":620},"A^T A",[574,1941,1943],{"className":1942,"ariaHidden":599},[625],[574,1944,1946,1949,1978],{"className":1945},[629],[574,1947],{"className":1948,"style":1135},[633],[574,1950,1952,1955],{"className":1951},[638],[574,1953,595],{"className":1954},[638,639],[574,1956,1958],{"className":1957},[978],[574,1959,1961],{"className":1960},[647],[574,1962,1964],{"className":1963},[651],[574,1965,1967],{"className":1966,"style":1135},[655],[574,1968,1969,1972],{"style":991},[574,1970],{"className":1971,"style":995},[662],[574,1973,1975],{"className":1974},[999,1000,1001,1002],[574,1976,1100],{"className":1977,"style":1165},[638,639,1002],[574,1979,595],{"className":1980},[638,639]," ist genau dann invertierbar, wenn die Spalten von ",[574,1983,1985,1998],{"className":1984},[577],[574,1986,1988],{"className":1987},[581],[583,1989,1990],{"xmlns":585},[587,1991,1992,1996],{},[590,1993,1994],{},[593,1995,595],{},[618,1997,595],{"encoding":620},[574,1999,2001],{"className":2000,"ariaHidden":599},[625],[574,2002,2004,2007],{"className":2003},[629],[574,2005],{"className":2006,"style":1380},[633],[574,2008,595],{"className":2009},[638,639]," linear unabhängig sind (",[574,2012,2014,2046],{"className":2013},[577],[574,2015,2017],{"className":2016},[581],[583,2018,2019],{"xmlns":585},[587,2020,2021,2043],{},[590,2022,2023,2027,2030,2033,2035,2038,2040],{},[593,2024,2026],{"mathvariant":2025},"normal","rg",[604,2028,2029],{},"⁡",[604,2031,2032],{"stretchy":832},"(",[593,2034,595],{},[604,2036,2037],{"stretchy":832},")",[604,2039,609],{},[593,2041,2042],{},"n",[618,2044,2045],{"encoding":620},"\\operatorname{rg}(A) = n",[574,2047,2049,2082],{"className":2048,"ariaHidden":599},[625],[574,2050,2052,2055,2064,2067,2070,2073,2076,2079],{"className":2051},[629],[574,2053],{"className":2054,"style":872},[633],[574,2056,2059],{"className":2057},[2058],"mop",[574,2060,2026],{"className":2061,"style":2063},[638,2062],"mathrm","margin-right:0.0139em;",[574,2065,2032],{"className":2066},[876],[574,2068,595],{"className":2069},[638,639],[574,2071,2037],{"className":2072},[971],[574,2074],{"className":2075,"style":699},[698],[574,2077,609],{"className":2078},[703],[574,2080],{"className":2081,"style":699},[698],[574,2083,2085,2089],{"className":2084},[629],[574,2086],{"className":2087,"style":2088},[633],"height:0.4306em;",[574,2090,2042],{"className":2091},[638,639],"). Dann ist die Lösung eindeutig: ",[574,2094,2096,2149],{"className":2095},[577],[574,2097,2099],{"className":2098},[581],[583,2100,2101],{"xmlns":585},[587,2102,2103,2146],{},[590,2104,2105,2111,2113,2115,2121,2123,2134,2140],{},[597,2106,2107,2109],{"accent":599},[593,2108,602],{},[604,2110,606],{},[604,2112,609],{},[604,2114,2032],{"stretchy":832},[852,2116,2117,2119],{},[593,2118,595],{},[593,2120,1100],{},[593,2122,595],{},[852,2124,2125,2127],{},[604,2126,2037],{"stretchy":832},[590,2128,2129,2131],{},[604,2130,844],{},[857,2132,2133],{},"1",[852,2135,2136,2138],{},[593,2137,595],{},[593,2139,1100],{},[597,2141,2142,2144],{"accent":599},[593,2143,614],{},[604,2145,606],{},[618,2147,2148],{"encoding":620},"\\vec x = (A^T A)^{-1} A^T \\vec b",[574,2150,2152,2202],{"className":2151,"ariaHidden":599},[625],[574,2153,2155,2158,2193,2196,2199],{"className":2154},[629],[574,2156],{"className":2157,"style":634},[633],[574,2159,2161],{"className":2160},[638,643],[574,2162,2164],{"className":2163},[647],[574,2165,2167],{"className":2166},[651],[574,2168,2170,2178],{"className":2169,"style":634},[655],[574,2171,2172,2175],{"style":658},[574,2173],{"className":2174,"style":663},[662],[574,2176,602],{"className":2177},[638,639],[574,2179,2180,2183],{"style":658},[574,2181],{"className":2182,"style":663},[662],[574,2184,2186],{"className":2185,"style":676},[675],[574,2187,2189],{"className":2188,"style":681},[680],[683,2190,2191],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,2192],{"d":694},[574,2194],{"className":2195,"style":699},[698],[574,2197,609],{"className":2198},[703],[574,2200],{"className":2201,"style":699},[698],[574,2203,2205,2208,2211,2240,2243,2278,2307],{"className":2204},[629],[574,2206],{"className":2207,"style":932},[633],[574,2209,2032],{"className":2210},[876],[574,2212,2214,2217],{"className":2213},[638],[574,2215,595],{"className":2216},[638,639],[574,2218,2220],{"className":2219},[978],[574,2221,2223],{"className":2222},[647],[574,2224,2226],{"className":2225},[651],[574,2227,2229],{"className":2228,"style":1135},[655],[574,2230,2231,2234],{"style":991},[574,2232],{"className":2233,"style":995},[662],[574,2235,2237],{"className":2236},[999,1000,1001,1002],[574,2238,1100],{"className":2239,"style":1165},[638,639,1002],[574,2241,595],{"className":2242},[638,639],[574,2244,2246,2249],{"className":2245},[971],[574,2247,2037],{"className":2248},[971],[574,2250,2252],{"className":2251},[978],[574,2253,2255],{"className":2254},[647],[574,2256,2258],{"className":2257},[651],[574,2259,2261],{"className":2260,"style":988},[655],[574,2262,2263,2266],{"style":991},[574,2264],{"className":2265,"style":995},[662],[574,2267,2269],{"className":2268},[999,1000,1001,1002],[574,2270,2272,2275],{"className":2271},[638,1002],[574,2273,844],{"className":2274},[638,1002],[574,2276,2133],{"className":2277},[638,1002],[574,2279,2281,2284],{"className":2280},[638],[574,2282,595],{"className":2283},[638,639],[574,2285,2287],{"className":2286},[978],[574,2288,2290],{"className":2289},[647],[574,2291,2293],{"className":2292},[651],[574,2294,2296],{"className":2295,"style":1135},[655],[574,2297,2298,2301],{"style":991},[574,2299],{"className":2300,"style":995},[662],[574,2302,2304],{"className":2303},[999,1000,1001,1002],[574,2305,1100],{"className":2306,"style":1165},[638,639,1002],[574,2308,2310],{"className":2309},[638,643],[574,2311,2313],{"className":2312},[647],[574,2314,2316],{"className":2315},[651],[574,2317,2319,2327],{"className":2318,"style":713},[655],[574,2320,2321,2324],{"style":658},[574,2322],{"className":2323,"style":663},[662],[574,2325,614],{"className":2326},[638,639],[574,2328,2329,2332],{"style":736},[574,2330],{"className":2331,"style":663},[662],[574,2333,2335],{"className":2334,"style":743},[675],[574,2336,2338],{"className":2337,"style":681},[680],[683,2339,2340],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,2341],{"d":694},[565,2343,2344,2345,1081,2348,2523,2524,2672,2673,2771,2772,2800,2801,2939,2940,3003],{},"Die ",[569,2346,2347],{},"Ausgleichsgerade",[574,2349,2351,2388],{"className":2350},[577],[574,2352,2354],{"className":2353},[581],[583,2355,2356],{"xmlns":585},[587,2357,2358,2385],{},[590,2359,2360,2363,2365,2373,2376,2382],{},[593,2361,2362],{},"y",[604,2364,609],{},[2366,2367,2368,2371],"msub",{},[593,2369,2370],{},"c",[857,2372,1769],{},[604,2374,2375],{},"+",[2366,2377,2378,2380],{},[593,2379,2370],{},[857,2381,2133],{},[593,2383,2384],{},"t",[618,2386,2387],{"encoding":620},"y = c_0 + c_1 t",[574,2389,2391,2411,2473],{"className":2390,"ariaHidden":599},[625],[574,2392,2394,2398,2402,2405,2408],{"className":2393},[629],[574,2395],{"className":2396,"style":2397},[633],"height:0.625em;vertical-align:-0.1944em;",[574,2399,2362],{"className":2400,"style":2401},[638,639],"margin-right:0.0359em;",[574,2403],{"className":2404,"style":699},[698],[574,2406,609],{"className":2407},[703],[574,2409],{"className":2410,"style":699},[698],[574,2412,2414,2418,2464,2467,2470],{"className":2413},[629],[574,2415],{"className":2416,"style":2417},[633],"height:0.7333em;vertical-align:-0.15em;",[574,2419,2421,2424],{"className":2420},[638],[574,2422,2370],{"className":2423},[638,639],[574,2425,2427],{"className":2426},[978],[574,2428,2431,2455],{"className":2429},[647,2430],"vlist-t2",[574,2432,2434,2450],{"className":2433},[651],[574,2435,2438],{"className":2436,"style":2437},[655],"height:0.3011em;",[574,2439,2441,2444],{"style":2440},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[574,2442],{"className":2443,"style":995},[662],[574,2445,2447],{"className":2446},[999,1000,1001,1002],[574,2448,1769],{"className":2449},[638,1002],[574,2451,2454],{"className":2452},[2453],"vlist-s","​",[574,2456,2458],{"className":2457},[651],[574,2459,2462],{"className":2460,"style":2461},[655],"height:0.15em;",[574,2463],{},[574,2465],{"className":2466,"style":918},[698],[574,2468,2375],{"className":2469},[922],[574,2471],{"className":2472,"style":918},[698],[574,2474,2476,2480,2520],{"className":2475},[629],[574,2477],{"className":2478,"style":2479},[633],"height:0.7651em;vertical-align:-0.15em;",[574,2481,2483,2486],{"className":2482},[638],[574,2484,2370],{"className":2485},[638,639],[574,2487,2489],{"className":2488},[978],[574,2490,2492,2512],{"className":2491},[647,2430],[574,2493,2495,2509],{"className":2494},[651],[574,2496,2498],{"className":2497,"style":2437},[655],[574,2499,2500,2503],{"style":2440},[574,2501],{"className":2502,"style":995},[662],[574,2504,2506],{"className":2505},[999,1000,1001,1002],[574,2507,2133],{"className":2508},[638,1002],[574,2510,2454],{"className":2511},[2453],[574,2513,2515],{"className":2514},[651],[574,2516,2518],{"className":2517,"style":2461},[655],[574,2519],{},[574,2521,2384],{"className":2522},[638,639]," durch Messpunkte ",[574,2525,2527,2563],{"className":2526},[577],[574,2528,2530],{"className":2529},[581],[583,2531,2532],{"xmlns":585},[587,2533,2534,2560],{},[590,2535,2536,2538,2545,2548,2552,2558],{},[604,2537,2032],{"stretchy":832},[2366,2539,2540,2542],{},[593,2541,2384],{},[593,2543,2544],{},"k",[604,2546,2547],{"separator":599},",",[2549,2550,2551],"mtext",{}," ",[2366,2553,2554,2556],{},[593,2555,2362],{},[593,2557,2544],{},[604,2559,2037],{"stretchy":832},[618,2561,2562],{"encoding":620},"(t_k,\\ y_k)",[574,2564,2566],{"className":2565,"ariaHidden":599},[625],[574,2567,2569,2572,2575,2617,2621,2624,2628,2669],{"className":2568},[629],[574,2570],{"className":2571,"style":872},[633],[574,2573,2032],{"className":2574},[876],[574,2576,2578,2581],{"className":2577},[638],[574,2579,2384],{"className":2580},[638,639],[574,2582,2584],{"className":2583},[978],[574,2585,2587,2609],{"className":2586},[647,2430],[574,2588,2590,2606],{"className":2589},[651],[574,2591,2594],{"className":2592,"style":2593},[655],"height:0.3361em;",[574,2595,2596,2599],{"style":2440},[574,2597],{"className":2598,"style":995},[662],[574,2600,2602],{"className":2601},[999,1000,1001,1002],[574,2603,2544],{"className":2604,"style":2605},[638,639,1002],"margin-right:0.0315em;",[574,2607,2454],{"className":2608},[2453],[574,2610,2612],{"className":2611},[651],[574,2613,2615],{"className":2614,"style":2461},[655],[574,2616],{},[574,2618,2547],{"className":2619},[2620],"mpunct",[574,2622,2551],{"className":2623},[698],[574,2625],{"className":2626,"style":2627},[698],"margin-right:0.1667em;",[574,2629,2631,2634],{"className":2630},[638],[574,2632,2362],{"className":2633,"style":2401},[638,639],[574,2635,2637],{"className":2636},[978],[574,2638,2640,2661],{"className":2639},[647,2430],[574,2641,2643,2658],{"className":2642},[651],[574,2644,2646],{"className":2645,"style":2593},[655],[574,2647,2649,2652],{"style":2648},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[574,2650],{"className":2651,"style":995},[662],[574,2653,2655],{"className":2654},[999,1000,1001,1002],[574,2656,2544],{"className":2657,"style":2605},[638,639,1002],[574,2659,2454],{"className":2660},[2453],[574,2662,2664],{"className":2663},[651],[574,2665,2667],{"className":2666,"style":2461},[655],[574,2668],{},[574,2670,2037],{"className":2671},[971]," ist der Spezialfall mit Zeilen ",[574,2674,2676,2704],{"className":2675},[577],[574,2677,2679],{"className":2678},[581],[583,2680,2681],{"xmlns":585},[587,2682,2683,2701],{},[590,2684,2685,2687,2689,2691,2693,2699],{},[604,2686,2032],{"stretchy":832},[857,2688,2133],{},[604,2690,2547],{"separator":599},[2549,2692,2551],{},[2366,2694,2695,2697],{},[593,2696,2384],{},[593,2698,2544],{},[604,2700,2037],{"stretchy":832},[618,2702,2703],{"encoding":620},"(1,\\ t_k)",[574,2705,2707],{"className":2706,"ariaHidden":599},[625],[574,2708,2710,2713,2716,2719,2722,2725,2728,2768],{"className":2709},[629],[574,2711],{"className":2712,"style":872},[633],[574,2714,2032],{"className":2715},[876],[574,2717,2133],{"className":2718},[638],[574,2720,2547],{"className":2721},[2620],[574,2723,2551],{"className":2724},[698],[574,2726],{"className":2727,"style":2627},[698],[574,2729,2731,2734],{"className":2730},[638],[574,2732,2384],{"className":2733},[638,639],[574,2735,2737],{"className":2736},[978],[574,2738,2740,2760],{"className":2739},[647,2430],[574,2741,2743,2757],{"className":2742},[651],[574,2744,2746],{"className":2745,"style":2593},[655],[574,2747,2748,2751],{"style":2440},[574,2749],{"className":2750,"style":995},[662],[574,2752,2754],{"className":2753},[999,1000,1001,1002],[574,2755,2544],{"className":2756,"style":2605},[638,639,1002],[574,2758,2454],{"className":2759},[2453],[574,2761,2763],{"className":2762},[651],[574,2764,2766],{"className":2765,"style":2461},[655],[574,2767],{},[574,2769,2037],{"className":2770},[971]," in ",[574,2773,2775,2788],{"className":2774},[577],[574,2776,2778],{"className":2777},[581],[583,2779,2780],{"xmlns":585},[587,2781,2782,2786],{},[590,2783,2784],{},[593,2785,595],{},[618,2787,595],{"encoding":620},[574,2789,2791],{"className":2790,"ariaHidden":599},[625],[574,2792,2794,2797],{"className":2793},[629],[574,2795],{"className":2796,"style":1380},[633],[574,2798,595],{"className":2799},[638,639]," und ",[574,2802,2804,2834],{"className":2803},[577],[574,2805,2807],{"className":2806},[581],[583,2808,2809],{"xmlns":585},[587,2810,2811,2831],{},[590,2812,2813,2819,2821,2823,2829],{},[597,2814,2815,2817],{"accent":599},[593,2816,614],{},[604,2818,606],{},[604,2820,609],{},[604,2822,2032],{"stretchy":832},[2366,2824,2825,2827],{},[593,2826,2362],{},[593,2828,2544],{},[604,2830,2037],{"stretchy":832},[618,2832,2833],{"encoding":620},"\\vec b = (y_k)",[574,2835,2837,2887],{"className":2836,"ariaHidden":599},[625],[574,2838,2840,2843,2878,2881,2884],{"className":2839},[629],[574,2841],{"className":2842,"style":713},[633],[574,2844,2846],{"className":2845},[638,643],[574,2847,2849],{"className":2848},[647],[574,2850,2852],{"className":2851},[651],[574,2853,2855,2863],{"className":2854,"style":713},[655],[574,2856,2857,2860],{"style":658},[574,2858],{"className":2859,"style":663},[662],[574,2861,614],{"className":2862},[638,639],[574,2864,2865,2868],{"style":736},[574,2866],{"className":2867,"style":663},[662],[574,2869,2871],{"className":2870,"style":743},[675],[574,2872,2874],{"className":2873,"style":681},[680],[683,2875,2876],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,2877],{"d":694},[574,2879],{"className":2880,"style":699},[698],[574,2882,609],{"className":2883},[703],[574,2885],{"className":2886,"style":699},[698],[574,2888,2890,2893,2896,2936],{"className":2889},[629],[574,2891],{"className":2892,"style":872},[633],[574,2894,2032],{"className":2895},[876],[574,2897,2899,2902],{"className":2898},[638],[574,2900,2362],{"className":2901,"style":2401},[638,639],[574,2903,2905],{"className":2904},[978],[574,2906,2908,2928],{"className":2907},[647,2430],[574,2909,2911,2925],{"className":2910},[651],[574,2912,2914],{"className":2913,"style":2593},[655],[574,2915,2916,2919],{"style":2648},[574,2917],{"className":2918,"style":995},[662],[574,2920,2922],{"className":2921},[999,1000,1001,1002],[574,2923,2544],{"className":2924,"style":2605},[638,639,1002],[574,2926,2454],{"className":2927},[2453],[574,2929,2931],{"className":2930},[651],[574,2932,2934],{"className":2933,"style":2461},[655],[574,2935],{},[574,2937,2037],{"className":2938},[971],". Für schlecht konditionierte Probleme rechnet man numerisch besser mit der QR-Zerlegung, weil 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liefert ",[574,4709,4711,4738],{"className":4710},[577],[574,4712,4714],{"className":4713},[581],[583,4715,4716],{"xmlns":585},[587,4717,4718,4735],{},[590,4719,4720,4726,4728],{},[2366,4721,4722,4724],{},[593,4723,2370],{},[857,4725,2133],{},[604,4727,609],{},[4729,4730,4731,4733],"mfrac",{},[857,4732,3254],{},[857,4734,859],{},[618,4736,4737],{"encoding":620},"c_1 = 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= 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Die Gerade lautet ",[574,5045,5047,5079],{"className":5046},[577],[574,5048,5050],{"className":5049},[581],[583,5051,5052],{"xmlns":585},[587,5053,5054,5076],{},[590,5055,5056,5058,5060,5066,5068,5074],{},[593,5057,2362],{},[604,5059,609],{},[4729,5061,5062,5064],{},[857,5063,4904],{},[857,5065,4907],{},[604,5067,2375],{},[4729,5069,5070,5072],{},[857,5071,3254],{},[857,5073,859],{},[593,5075,2384],{},[618,5077,5078],{"encoding":620},"y = \\frac76 + \\frac32 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Probe: 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\\vec r = \\left(-\\frac16 + \\frac13 - \\frac16,\\ \\frac13 - \\frac26\\right) = (0,\\ 0)",[574,5719,5721,5800,6209],{"className":5720,"ariaHidden":599},[625],[574,5722,5724,5727,5756,5791,5794,5797],{"className":5723},[629],[574,5725],{"className":5726,"style":1135},[633],[574,5728,5730,5733],{"className":5729},[638],[574,5731,595],{"className":5732},[638,639],[574,5734,5736],{"className":5735},[978],[574,5737,5739],{"className":5738},[647],[574,5740,5742],{"className":5741},[651],[574,5743,5745],{"className":5744,"style":1135},[655],[574,5746,5747,5750],{"style":991},[574,5748],{"className":5749,"style":995},[662],[574,5751,5753],{"className":5752},[999,1000,1001,1002],[574,5754,1100],{"className":5755,"style":1165},[638,639,1002],[574,5757,5759],{"className":5758},[638,643],[574,5760,5762],{"className":5761},[647],[574,5763,5765],{"className":5764},[651],[574,5766,5768,5776],{"className":5767,"style":634},[655],[574,5769,5770,5773],{"style":658},[574,5771],{"className":5772,"style":663},[662],[574,5774,1535],{"className":5775,"style":1588},[638,639],[574,5777,5778,5781],{"style":658},[574,5779],{"className":5780,"style":663},[662],[574,5782,5784],{"className":5783,"style":1597},[675],[574,5785,5787],{"className":5786,"style":681},[680],[683,5788,5789],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,5790],{"d":694},[574,5792],{"className":5793,"style":699},[698],[574,5795,609],{"className":5796},[703],[574,5798],{"className":5799,"style":699},[698],[574,5801,5803,5806,6200,6203,6206],{"className":5802},[629],[574,5804],{"className":5805,"style":5381},[633],[574,5807,5809,5815,5818,5886,5889,5892,5895,5963,5966,5969,5972,6040,6043,6046,6049,6117,6120,6123,6126,6194],{"className":5808},[3611],[574,5810,5812],{"className":5811,"style":4099},[876,4098],[574,5813,2032],{"className":5814},[3618,5391],[574,5816,844],{"className":5817},[638],[574,5819,5821,5824,5883],{"className":5820},[638],[574,5822],{"className":5823},[876,4810],[574,5825,5827],{"className":5826},[4729],[574,5828,5830,5875],{"className":5829},[647,2430],[574,5831,5833,5872],{"className":5832},[651],[574,5834,5836,5850,5858],{"className":5835,"style":4823},[655],[574,5837,5838,5841],{"style":4826},[574,5839],{"className":5840,"style":663},[662],[574,5842,5844],{"className":5843},[999,1000,1001,1002],[574,5845,5847],{"className":5846},[638,1002],[574,5848,4907],{"className":5849},[638,1002],[574,5851,5852,5855],{"style":4841},[574,5853],{"className":5854,"style":663},[662],[574,5856],{"className":5857,"style":4849},[4848],[574,5859,5860,5863],{"style":4852},[574,5861],{"className":5862,"style":663},[662],[574,5864,5866],{"className":5865},[999,1000,1001,1002],[574,5867,5869],{"className":5868},[638,1002],[574,5870,2133],{"className":5871},[638,1002],[574,5873,2454],{"className":5874},[2453],[574,5876,5878],{"className":5877},[651],[574,5879,5881],{"className":5880,"style":4874},[655],[574,5882],{},[574,5884],{"className":5885},[971,4810],[574,5887],{"className":5888,"style":918},[698],[574,5890,2375],{"className":5891},[922],[574,5893],{"className":5894,"style":918},[698],[574,5896,5898,5901,5960],{"className":5897},[638],[574,5899],{"className":5900},[876,4810],[574,5902,5904],{"className":5903},[4729],[574,5905,5907,5952],{"className":5906},[647,2430],[574,5908,5910,5949],{"className":5909},[651],[574,5911,5913,5927,5935],{"className":5912,"style":4823},[655],[574,5914,5915,5918],{"style":4826},[574,5916],{"className":5917,"style":663},[662],[574,5919,5921],{"className":5920},[999,1000,1001,1002],[574,5922,5924],{"className":5923},[638,1002],[574,5925,3254],{"className":5926},[638,1002],[574,5928,5929,5932],{"style":4841},[574,5930],{"className":5931,"style":663},[662],[574,5933],{"className":5934,"style":4849},[4848],[574,5936,5937,5940],{"style":4852},[574,5938],{"className":5939,"style":663},[662],[574,5941,5943],{"className":5942},[999,1000,1001,1002],[574,5944,5946],{"className":5945},[638,1002],[574,5947,2133],{"className":5948},[638,1002],[574,5950,2454],{"className":5951},[2453],[574,5953,5955],{"className":5954},[651],[574,5956,5958],{"className":5957,"style":4874},[655],[574,5959],{},[574,5961],{"className":5962},[971,4810],[574,5964],{"className":5965,"style":918},[698],[574,5967,844],{"className":5968},[922],[574,5970],{"className":5971,"style":918},[698],[574,5973,5975,5978,6037],{"className":5974},[638],[574,5976],{"className":5977},[876,4810],[574,5979,5981],{"className":5980},[4729],[574,5982,5984,6029],{"className":5983},[647,2430],[574,5985,5987,6026],{"className":5986},[651],[574,5988,5990,6004,6012],{"className":5989,"style":4823},[655],[574,5991,5992,5995],{"style":4826},[574,5993],{"className":5994,"style":663},[662],[574,5996,5998],{"className":5997},[999,1000,1001,1002],[574,5999,6001],{"className":6000},[638,1002],[574,6002,4907],{"className":6003},[638,1002],[574,6005,6006,6009],{"style":4841},[574,6007],{"className":6008,"style":663},[662],[574,6010],{"className":6011,"style":4849},[4848],[574,6013,6014,6017],{"style":4852},[574,6015],{"className":6016,"s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Die minimale Fehlerquadratsumme ist ",[574,6238,6240,6274],{"className":6239},[577],[574,6241,6243],{"className":6242},[581],[583,6244,6245],{"xmlns":585},[587,6246,6247,6271],{},[590,6248,6249,6251,6257,6263,6265],{},[604,6250,833],{"stretchy":832},[597,6252,6253,6255],{"accent":599},[593,6254,1535],{},[604,6256,606],{},[852,6258,6259,6261],{},[604,6260,833],{"stretchy":832},[857,6262,859],{},[604,6264,609],{},[4729,6266,6267,6269],{},[857,6268,2133],{},[857,6270,4907],{},[618,6272,6273],{"encoding":620},"\\lVert \\vec r \\rVert^2 = \\frac16",[574,6275,6277,6360],{"className":6276,"ariaHidden":599},[625],[574,6278,6280,6284,6287,6322,6351,6354,6357],{"className":6279},[629],[574,6281],{"className":6282,"style":6283},[633],"height:1.0641em;vertical-align:-0.25em;",[574,6285,833],{"className":6286},[876],[574,6288,6290],{"className":6289},[638,643],[574,6291,6293],{"className":6292},[647],[574,6294,6296],{"className":6295},[651],[574,6297,6299,6307],{"className":6298,"style":634},[655],[574,6300,6301,6304],{"style":658},[574,6302],{"className":6303,"style":663},[662],[574,6305,1535],{"className":6306,"style":1588},[638,639],[574,6308,6309,6312],{"style":658},[574,6310],{"className":6311,"style":663},[662],[574,6313,6315],{"className":6314,"style":1597},[675],[574,6316,6318],{"className":6317,"style":681},[680],[683,6319,6320],{"xmlns":685,"width":686,"height":687,"style":688,"viewBox":689,"preserveAspectRatio":690},[692,6321],{"d":694},[574,6323,6325,6328],{"className":6324},[971],[574,6326,833],{"className":6327},[971],[574,6329,6331],{"className":6330},[978],[574,6332,6334],{"className":6333},[647],[574,6335,6337],{"className":6336},[651],[574,6338,6340],{"className":6339,"style":988},[655],[574,6341,6342,6345],{"style":991},[574,6343],{"className":6344,"style":995},[662],[574,6346,6348],{"className":6347},[999,1000,1001,1002],[574,6349,859],{"className":6350},[638,1002],[574,6352],{"className":6353,"style":699},[698],[574,6355,609],{"className":6356},[703],[574,6358],{"className":6359,"style":699},[698],[574,6361,6363,6366],{"className":6362},[629],[574,6364],{"className":6365,"style":4803},[633],[574,6367,6369,6372,6431],{"className":6368},[638],[574,6370],{"className":6371},[876,4810],[574,6373,6375],{"className":6374},[4729],[574,6376,6378,6423],{"className":6377},[647,2430],[574,6379,6381,6420],{"className":6380},[651],[574,6382,6384,6398,6406],{"className":6383,"style":4823},[655],[574,6385,6386,6389],{"style":4826},[574,6387],{"className":6388,"style":663},[662],[574,6390,6392],{"className":6391},[999,1000,1001,1002],[574,6393,6395],{"className":6394},[638,1002],[574,6396,4907],{"className":6397},[638,1002],[574,6399,6400,6403],{"style":4841},[574,6401],{"className":6402,"style":663},[662],[574,6404],{"className":6405,"style":4849},[4848],[574,6407,6408,6411],{"style":4852},[574,6409],{"className":6410,"style":663},[662],[574,6412,6414],{"className":6413},[999,1000,1001,1002],[574,6415,6417],{"className":6416},[638,1002],[574,6418,2133],{"className":6419},[638,1002],[574,6421,2454],{"className":6422},[2453],[574,6424,6426],{"className":6425},[651],[574,6427,6429],{"className":6428,"style":4874},[655],[574,6430],{},[574,6432],{"className":6433},[971,4810],[565,6435,6436,6437,6489,6490,1009],{},"Als Vorhersage für ",[574,6438,6440,6458],{"className":6439},[577],[574,6441,6443],{"className":6442},[581],[583,6444,6445],{"xmlns":585},[587,6446,6447,6455],{},[590,6448,6449,6451,6453],{},[593,6450,2384],{},[604,6452,609],{},[857,6454,3254],{},[618,6456,6457],{"encoding":620},"t = 3",[574,6459,6461,6480],{"className":6460,"ariaHidden":599},[625],[574,6462,6464,6468,6471,6474,6477],{"className":6463},[629],[574,6465],{"className":6466,"style":6467},[633],"height:0.6151em;",[574,6469,2384],{"className":6470},[638,639],[574,6472],{"className":6473,"style":699},[698],[574,6475,609],{"className":6476},[703],[574,6478],{"className":6479,"style":699},[698],[574,6481,6483,6486],{"className":6482},[629],[574,6484],{"className":6485,"style":4538},[633],[574,6487,3254],{"className":6488},[638]," ergibt sich 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direkt mit dem Gauß-Algorithmus lösen wollen. Es ist in der Regel widersprüchlich.",[1908,6967,6968,7032,7033,7096,7097,7160,7161,7215,7216,1009],{},[574,6969,6971,6991],{"className":6970},[577],[574,6972,6974],{"className":6973},[581],[583,6975,6976],{"xmlns":585},[587,6977,6978,6988],{},[590,6979,6980,6982],{},[593,6981,595],{},[852,6983,6984,6986],{},[593,6985,595],{},[593,6987,1100],{},[618,6989,6990],{"encoding":620},"A A^T",[574,6992,6994],{"className":6993,"ariaHidden":599},[625],[574,6995,6997,7000,7003],{"className":6996},[629],[574,6998],{"className":6999,"style":1135},[633],[574,7001,595],{"className":7002},[638,639],[574,7004,7006,7009],{"className":7005},[638],[574,7007,595],{"className":7008},[638,639],[574,7010,7012],{"className":7011},[978],[574,7013,7015],{"className":7014},[647],[574,7016,7018],{"className":7017},[651],[574,7019,7021],{"className":7020,"style":1135},[655],[574,7022,7023,7026],{"style":991},[574,7024],{"className":7025,"style":995},[662],[574,7027,7029],{"className":7028},[999,1000,1001,1002],[574,7030,1100],{"className":7031,"style":1165},[638,639,1002]," statt ",[574,7034,7036,7055],{"className":7035},[577],[574,7037,7039],{"className":7038},[581],[583,7040,7041],{"xmlns":585},[587,7042,7043,7053],{},[590,7044,7045,7051],{},[852,7046,7047,7049],{},[593,7048,595],{},[593,7050,1100],{},[593,7052,595],{},[618,7054,1939],{"encoding":620},[574,7056,7058],{"className":7057,"ariaHidden":599},[625],[574,7059,7061,7064,7093],{"className":7060},[629],[574,7062],{"className":7063,"style":1135},[633],[574,7065,7067,7070],{"className":7066},[638],[574,7068,595],{"className":7069},[638,639],[574,7071,7073],{"className":7072},[978],[574,7074,7076],{"className":7075},[647],[574,7077,7079],{"className":7078},[651],[574,7080,7082],{"className":7081,"style":1135},[655],[574,7083,7084,7087],{"style":991},[574,7085],{"className":7086,"style":995},[662],[574,7088,7090],{"className":7089},[999,1000,1001,1002],[574,7091,1100],{"className":7092,"style":1165},[638,639,1002],[574,7094,595],{"className":7095},[638,639]," bilden. 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vergessen und nur 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einsetzen.",[1908,7510,7511,7773,7774,7802,7803,1009],{},[574,7512,7514,7576],{"className":7513},[577],[574,7515,7517],{"className":7516},[581],[583,7518,7519],{"xmlns":585},[587,7520,7521,7573],{},[590,7522,7523,7525,7531,7533,7543,7545,7555,7557,7563],{},[604,7524,2032],{"stretchy":832},[852,7526,7527,7529],{},[593,7528,595],{},[593,7530,1100],{},[593,7532,595],{},[852,7534,7535,7537],{},[604,7536,2037],{"stretchy":832},[590,7538,7539,7541],{},[604,7540,844],{},[857,7542,2133],{},[604,7544,609],{},[852,7546,7547,7549],{},[593,7548,595],{},[590,7550,7551,7553],{},[604,7552,844],{},[857,7554,2133],{},[604,7556,2032],{"stretchy":832},[852,7558,7559,7561],{},[593,7560,595],{},[593,7562,1100],{},[852,7564,7565,7567],{},[604,7566,2037],{"stretchy":832},[590,7568,7569,7571],{},[604,7570,844],{},[857,7572,2133],{},[618,7574,7575],{"encoding":620},"(A^T A)^{-1} = A^{-1} (A^T)^{-1}",[574,7577,7579,7665],{"className":7578,"ariaHidden":599},[625],[574,7580,7582,7586,7589,7618,7621,7656,7659,7662],{"className":7581},[629],[574,7583],{"className":7584,"style":7585},[633],"height:1.0913em;vertical-align:-0.25em;",[574,7587,2032],{"className":7588},[876],[574,7590,7592,7595],{"className":7591},[638],[574,7593,595],{"className":7594},[638,639],[574,7596,7598],{"className":7597},[978],[574,7599,7601],{"className":7600},[647],[574,7602,7604],{"className":7603},[651],[574,7605,7607],{"className":7606,"style":1135},[655],[574,7608,7609,7612],{"style":991},[574,7610],{"className":7611,"style":995},[662],[574,7613,7615],{"className":7614},[999,1000,1001,1002],[574,7616,1100],{"className":7617,"style":1165},[638,639,1002],[574,7619,595],{"className":7620},[638,639],[574,7622,7624,7627],{"className":7623},[971],[574,7625,2037],{"className":7626},[971],[574,7628,7630],{"className":7629},[978],[574,7631,7633],{"className":7632},[647],[574,7634,7636],{"className":7635},[651],[574,7637,7639],{"className":7638,"style":988},[655],[574,7640,7641,7644],{"style":991},[574,7642],{"className":7643,"style":995},[662],[574,7645,7647],{"className":7646},[999,1000,1001,1002],[574,7648,7650,7653],{"className":7649},[638,1002],[574,7651,844],{"className":7652},[638,1002],[574,7654,2133],{"className":7655},[638,1002],[574,7657],{"className":7658,"style":699},[698],[574,7660,609],{"className":7661},[703],[574,7663],{"className":7664,"style":699},[698],[574,7666,7668,7671,7706,7709,7738],{"className":7667},[629],[574,7669],{"className":7670,"style":7585},[633],[574,7672,7674,7677],{"className":7673},[638],[574,7675,595],{"className":7676},[638,639],[574,7678,7680],{"className":7679},[978],[574,7681,7683],{"className":7682},[647],[574,7684,7686],{"className":7685},[651],[574,7687,7689],{"className":7688,"style":988},[655],[574,7690,7691,7694],{"style":991},[574,7692],{"className":7693,"style":995},[662],[574,7695,7697],{"className":7696},[999,1000,1001,1002],[574,7698,7700,7703],{"className":7699},[638,1002],[574,7701,844],{"className":7702},[638,1002],[574,7704,2133],{"className":7705},[638,1002],[574,7707,2032],{"className":7708},[876],[574,7710,7712,7715],{"className":7711},[638],[574,7713,595],{"className":7714},[638,639],[574,7716,7718],{"className":7717},[978],[574,7719,7721],{"className":7720},[647],[574,7722,7724],{"className":7723},[651],[574,7725,7727],{"className":7726,"style":1135},[655],[574,7728,7729,7732],{"style":991},[574,7730],{"className":7731,"style":995},[662],[574,7733,7735],{"className":7734},[999,1000,1001,1002],[574,7736,1100],{"className":7737,"style":1165},[638,639,1002],[574,7739,7741,7744],{"className":7740},[971],[574,7742,2037],{"className":7743},[971],[574,7745,7747],{"className":7746},[978],[574,7748,7750],{"className":7749},[647],[574,7751,7753],{"className":7752},[651],[574,7754,7756],{"className":7755,"style":988},[655],[574,7757,7758,7761],{"style":991},[574,7759],{"className":7760,"style":995},[662],[574,7762,7764],{"className":7763},[999,1000,1001,1002],[574,7765,7767,7770],{"className":7766},[638,1002],[574,7768,844],{"className":7769},[638,1002],[574,7771,2133],{"className":7772},[638,1002]," ansetzen. Für nicht quadratisches ",[574,7775,7777,7790],{"className":7776},[577],[574,7778,7780],{"className":7779},[581],[583,7781,7782],{"xmlns":585},[587,7783,7784,7788],{},[590,7785,7786],{},[593,7787,595],{},[618,7789,595],{"encoding":620},[574,7791,7793],{"className":7792,"ariaHidden":599},[625],[574,7794,7796,7799],{"className":7795},[629],[574,7797],{"className":7798,"style":1380},[633],[574,7800,595],{"className":7801},[638,639]," gibt es kein ",[574,7804,7806,7828],{"className":7805},[577],[574,7807,7809],{"className":7808},[581],[583,7810,7811],{"xmlns":585},[587,7812,7813,7825],{},[590,7814,7815],{},[852,7816,7817,7819],{},[593,7818,595],{},[590,7820,7821,7823],{},[604,7822,844],{},[857,7824,2133],{},[618,7826,7827],{"encoding":620},"A^{-1}",[574,7829,7831],{"className":7830,"ariaHidden":599},[625],[574,7832,7834,7837],{"className":7833},[629],[574,7835],{"className":7836,"style":988},[633],[574,7838,7840,7843],{"className":7839},[638],[574,7841,595],{"className":7842},[638,639],[574,7844,7846],{"className":7845},[978],[574,7847,7849],{"className":7848},[647],[574,7850,7852],{"className":7851},[651],[574,7853,7855],{"className":7854,"style":988},[655],[574,7856,7857,7860],{"style":991},[574,7858],{"className":7859,"style":995},[662],[574,7861,7863],{"className":7862},[999,1000,1001,1002],[574,7864,7866,7869],{"className":7865},[638,1002],[574,7867,844],{"className":7868},[638,1002],[574,7870,2133],{"className":7871},[638,1002],{"title":7873,"searchDepth":7874,"depth":7874,"links":7875},"",2,[7876,7877,7878],{"id":562,"depth":7874,"text":563},{"id":3006,"depth":7874,"text":3007},{"id":6831,"depth":7874,"text":6832},[7880,7882,7884,7886,7888,7890,7892,7894,7897,7900,7903,7906,7908,7910,7912,7915,7918],{"lhs":7881,"rhs":3254},"multiply(transpose([[1, 0], [1, 1], [1, 2]]), [[1, 0], [1, 1], [1, 2]])[1, 1]",{"lhs":7883,"rhs":3254},"multiply(transpose([[1, 0], [1, 1], [1, 2]]), [[1, 0], [1, 1], [1, 2]])[1, 2]",{"lhs":7885,"rhs":3530},"multiply(transpose([[1, 0], [1, 1], [1, 2]]), [[1, 0], [1, 1], [1, 2]])[2, 2]",{"lhs":7887,"rhs":3565},"multiply(transpose([[1, 0], [1, 1], [1, 2]]), [1, 3, 4])[1]",{"lhs":7889,"rhs":3574},"multiply(transpose([[1, 0], [1, 1], [1, 2]]), [1, 3, 4])[2]",{"lhs":7891,"rhs":3565},"3*(7\u002F6) + 3*(3\u002F2)",{"lhs":7893,"rhs":3574},"3*(7\u002F6) + 5*(3\u002F2)",{"lhs":7895,"rhs":7896},"multiply(inv([[3, 3], [3, 5]]), [8, 11])[1]","7\u002F6",{"lhs":7898,"rhs":7899},"multiply(inv([[3, 3], [3, 5]]), [8, 11])[2]","3\u002F2",{"lhs":7901,"rhs":7902},"1 - 7\u002F6","-1\u002F6",{"lhs":7904,"rhs":7905},"3 - (7\u002F6 + 3\u002F2)","1\u002F3",{"lhs":7907,"rhs":7902},"4 - (7\u002F6 + 2*3\u002F2)",{"lhs":7909,"rhs":1769},"-1\u002F6 + 1\u002F3 - 1\u002F6",{"lhs":7911,"rhs":1769},"0*(-1\u002F6) + 1*(1\u002F3) + 2*(-1\u002F6)",{"lhs":7913,"rhs":7914},"(-1\u002F6)^2 + (1\u002F3)^2 + (-1\u002F6)^2","1\u002F6",{"lhs":7916,"rhs":7917},"7\u002F6 + 3\u002F2*3","17\u002F3",{"lhs":7919,"rhs":7920},"round(17\u002F3, 2)","5.67","A \\in \\mathbb{R}^{m \\times n},\\ \\vec b \\in \\mathbb{R}^{m}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{m \\times n},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec b \\in \\mathbb{R}^{m}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0165em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","normal-equations","A^{T} A\\, \\vec x = A^{T} \\vec b","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{T} A\\, \\vec x = A^{T} \\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:0.8913em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:0.9774em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" 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