00
5求下列矩阵的秩并求一个最高阶非零子式求下列矩阵的秩并求一个最高阶非零子式并求一个最高阶非零子式02313213122131311121134470518
3
218230325103
77580203
3
f02112131r1r202解11121311344134411211121r3r2r23r104650465秩为2r3r10000046531二阶子式411r1r231443213221r2r122131307119570518r37r1021332715134413r2071195秩为2r30000032二阶子式721
21823033251030r23r10r32r101
12000003
701r12r4750380r22r40220r3r1034r1r21710r4r101601014r3÷140020r÷160043
176354203202
0217秩为300100032
r4r307558三阶子式580570≠032320
6求解下列齐次线性方程组求解下列齐次线性方程组
4
f1
3
解
122
x1x22x3x40x12x2x3x4023x16x2x33x402x1x2x3x402x2xx2x05x10xx5x0234234112x13x2x35x403x14x25x37x403x2x3x3x2x01x22x37x401234444x1x23x36x404x111x213x316x40x12x24x37x407x12x2x33x40对系数矩阵实施行变换1对系数矩阵实施行变换4x1x431211010x23x41110131即得4x4x2120013343xx44
4x13x2故方程组的解为k43x33x14
对系数矩阵实施行变换2对系数矩阵实施行变换
1213615101
112013001050000
x1x2即得x3x4
2x2x4x20x4
x121x210故方程组的解为k1k2x00301x4
对系数矩阵实施行变换3对系数矩阵实施行变换
5
f23151312704136012470x10x20故方程组的解为x30x40
0100
0010
x10x02即得0x3x41
0000
对系数矩阵实施行变换4对系数矩阵实施行变换3137105341717192032230117174111316000072130000313x1x3x417171920x3x4即得x21717x3x3xx44313x11717x21920故方程组的解为k1k21717x310x4017求解下列非齐次线性方程组求解下列非齐次线性方程组
4x12x2x32r