Question

用初等行变换求下列矩阵的逆矩阵的详细步骤

「1 2 2
2 1 -2
2 -2 1」

Answer 1

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

r2-2r1, r3-2r1
1 2 2 1 0 0
0 -3 -6 -2 1 0
0 -6 -3 -2 0 1

r3-2r2
1 2 2 1 0 0
0 -3 -6 -2 1 0
0 0 9 2 -2 1

r3*(1/9)
1 2 2 1 0 0
0 -3 -6 -2 1 0
0 0 1 2/9 -2/9 1/9

r1-2r3, r2+6r3
1 2 0 5/9 4/9 -2/9
0 -3 0 -6/9 -3/9 6/9
0 0 1 2/9 -2/9 1/9

r2*(-1/3), r1-2r2
1 0 0 1/9 2/9 2/9
0 1 0 2/9 1/9 -2/9
0 0 1 2/9 -2/9 1/9

满意请采纳 ^_^