Question

如何利用行初等变换吧A矩阵变为单位矩阵?

Answer 1

1+r2+r3+r4

4 0 0 0

1 1 -1 -1

1 -1 1 -1

1 -1 -1 1

r1*(1/4),r2-r1,r3-r1,r4-r1

1 0 0 0

0 1 -1 -1

0 -1 1 -1

0 -1 -1 1

r3+r2,r4+r2

1 0 0 0

0 1 -1 -1

0 0 0 -2

0 0 -2 0

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

1 0 0 0

0 1 0 0

0 0 0 1

0 0 1 0

r3r4

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1