线性代数第三章习题解答
１用消元法解下列线性方程组
2x1x23x333xx5x012314x1x2x33x13x213x36
解对原线性方程组的增广矩阵做初等行变换化成阶梯形：
23A41
131511313
3230r32r13061
131515313
3230r2r33061
130015313
331r3236
21010100
130015313
1000
3010
3011r4r20r12r23601101r1r2011r23r300000
130015313
0010
101101r43r100r3r13700110012r20102．1001100000
3024
11r42r3r23214
由此可得原线性方程组的解是x1x2x3T121T．
2
2x1x2x3x413x12x2x33x44x14x23x35x42
对原线性方程组的增广矩阵做初等行变换化成阶梯形：
解
211110759514352r12r3r22r1A321340141018100000014352r23r314352r1r307595
1430005017
1r37
52009577
1161161077710777595r2r30000001r14r37770000001595777
由此可得原线性方程组的一般解是
116x17x37x47，x3x4是自由未知数．595x2x3x4777
fx12x2x3x413x12x2x3x41x12x2x35x45
解对原线性方程组的增广矩阵做初等行变换化成阶梯形：
121111211112111r33r2r2r1121110002200022，12155r3r100064000010
因为系数矩阵的秩是２，增广矩阵的秩是３，所以原方程组无解．2已知向量r