3
2λx12x22x3110设2x15λx24x322x4x5λxλ1123为何值时此方程组有唯一解无解或有无穷多解此方程组有唯一解问λ为何值时此方程组有唯一解无解或有无穷多解并在有无穷多解时求解时求解2122λ5λ42解2245λλ15λ12初等行变换121λ1λ01λ1λ10λ1λ4λ00221λ210λ当A≠0即即≠0∴λ≠1且λ≠10时有唯一解有唯一解21λ10λ1λ4λ无解当0且≠0即λ10时无解22
9
f1λ10λ1λ4λ有无穷多解0且0即λ1时有无穷多解221221此时此时增广矩阵为00000000
当
x1221原方程组的解为x2k11k200010x3
k1k2∈R
11试利用矩阵的初等变换求下列方阵的逆矩阵试利用矩阵的初等变换求下列方阵的逆矩阵320132121021315212323230121321100321100解131501001411032300100210179312030032022220101120101121100210100102272310063201011210011022237326故逆矩阵为11211022
10
f000010011001302210100023200112100010111034021010202320011210001011103400121610200112210001010101136001216100001124100010101011360012161012411010故逆矩阵为611321610
3021010001000100010001000
20110221012320012100232001210049510
41213121设A221B22求X使AXB求31131
11
f2101232设A213B231求X使XAB求334
解
241213初等行变换10010AB221221010153311310011242101∴XAB153124
21012130初等列变换0A3342B12322314211∴XBA1474
0111740010
12
fr