Question

设矩阵A=5 0 0 求矩阵A^-1 0 1 4 1 2 7,

Answer 1

A=

5 0 0

0 1 4

1 2 7

(A,E)=

5 0 0 1 0 0

0 1 4 0 1 0

1 2 7 0 0 1

r3-2r2

5 0 0 1 0 0

0 1 4 0 1 0

1 0 -1 0 -2 1

r1-5r3

0 0 5 1 10 -5

0 1 4 0 1 0

1 0 -1 0 -2 1

r1*(1/5)

0 0 1 1/5 2 -1

0 1 4 0 1 0

1 0 -1 0 -2 1

r2-4r1,r3+r1

0 0 1 1/5 2 -1

0 1 0 -4/5 -7 4

1 0 0 1/5 0 0

r1r3

1 0 0 1/5 0 0

0 1 0 -4/5 -7 4

0 0 1 1/5 2 -1

A的逆为

1/5 0 0

-4/5 -7 4

1/5 2 -1