Question

线性代数第四版 赵树嫄 的 103页的54的3 和 104页的55的2 发 gringoirejyc@ya

Answer 1

2+r1,r3+r1,r4+r1

1 1 1 1 1 0 0 0

0 2 2 2 1 1 0 0

0 0 2 2 1 0 1 0

0 0 0 2 1 0 0 1

r2*(1/2),r3*(1/2),r4*(1/2),

1 1 1 1 1 0 0 0

0 1 1 1 1/2 1/2 0 0

0 0 1 1 1/2 0 1/2 0

0 0 0 1 1/2 0 0 1/2

r1-r2,r2-r3,r3-r4

1 0 0 0 1/2 -1/2 0 0

0 1 0 0 0 1/2 -1/2 0

0 0 1 0 0 0 1/2 -1/2

0 0 0 1 1/2 0 0 1/2

55(2)

解: (A,B)=

1 1 -1 1

0 2 -5 2

1 0 1 3

r3-r1

1 1 -1 1

0 2 -5 2

0 -1 2 2

r1+r3,r2+2r3,r3*(-1)

1 0 1 3

0 0 -1 6

0 1 -2 -2

r1+r2,r3-2r2

1 0 0 9

0 0 -1 6

0 1 0 -14

r2*(-1),r2r3

1 0 0 9

0 1 0 -14

0 0 1 -6

所以 X=(9,-14,-6)^T.