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计算逆矩阵要过程1 2 -5 11 -3 0 -60 2 -1 21 4 -7 6

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计算逆矩阵要过程
1 2 -5 1
1 -3 0 -6
0 2 -1 2
1 4 -7 6
计算逆矩阵要过程1 2 -5 11 -3 0 -60 2 -1 21 4 -7 6
利用初等变换求逆矩阵(A,E)→(E,A^-1)
1 2 -5 1 1 0 0 0
1 -3 0 -6 0 1 0 0
0 2 -1 2 0 0 1 0
1 4 -7 6 0 0 0 1
r2-r1,r4-r1
1 2 -5 1 1 0 0 0
0 -5 5 -7 -1 1 0 0
0 2 -1 2 0 0 1 0
0 2 -2 5 -1 0 0 1
r1-r3,r4-r3,r2+3r3
1 0 -4 -1 1 0 -1 0
0 1 2 -1 -1 1 3 0
0 2 -1 2 0 0 1 0
0 0 -1 3 -1 0 -1 1
r3-2r2
1 0 -4 -1 1 0 -1 0
0 1 2 -1 -1 1 3 0
0 0 -5 4 2 -2 -5 0
0 0 -1 3 -1 0 -1 1
r3r4,-r3
1 0 -4 -1 1 0 -1 0
0 1 2 -1 -1 1 3 0
0 0 1 -3 1 0 1 -1
0 0 -5 4 2 -2 -5 0
r4+5r3,r1+4r3,r2-2r3,-1/11 r4
1 0 0 -13 5 0 3 -4
0 1 0 5 -3 1 1 2
0 0 1 -3 1 0 1 -1
0 0 0 1 -7/11 2/11 0 5/11
r1+13r4,r2-5r4,r3+3r4
1 0 0 0 -36/11 26/11 3 21/11
0 1 0 0 -68/11 1/11 1 -3/11
0 0 1 0 10/11 6/11 1 4/11
0 0 0 1 -7/11 2/11 0 5/11
所以逆矩阵为
-36/11 26/11 3 21/11
-68/11 1/11 1 -3/11
10/11 6/11 1 4/11
-7/11 2/11 0 5/11