Question

把矩阵(1 2 -1 0)(2 -1 3 1)(4 3 1 -1)(1 -3 5 1)化成行最简形.

Answer 1

1 2 -1 0

2 -1 3 1

4 3 1 -1

1 -3 5 1

r2-2r1,r3-4r1,r4-r1得

1 2 -1 0

0 -5 5 1

0 -5 5 -1

0 -5 6 1

r3-r2,r4-r2得

1 2 -1 0

0 -5 5 1

0 0 0 -2

0 0 1 0

r3和r4对调得

1 2 -1 0

0 -5 5 1

0 0 1 0

0 0 0 -2

r2×(-1/5),r4×(-1/2)得

1 2 -1 0

0 1 -1 -1/5

0 0 1 0

0 0 0 1