系数矩阵A为1-21 21-3 -11-1等于多少?
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发布时间：2024-10-15 21:12
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时间：9分钟前
4、初等行变换求逆矩阵
这里即(A，E)=
0 1 2 1 1 0 0 0
3 -2 0 1 0 1 0 0
1 2 -3 -2 0 0 1 0
0 2 2 1 0 0 0 1 r2-3r3,r3-r4,r4-r1
~
0 1 2 1 1 0 0 0
0 -8 9 7 0 1 -3 0
1 0 -5 -3 0 0 1 -1
0 1 0 0 -1 0 0 1 r2+8r1，r1-r4,
~
0 0 2 1 2 0 0 -1
0 0 25 15 16 1 -3 -8
1 0 -5 -3 0 0 1 -1
0 1 0 0 -1 0 0 1 r3+r2 *1/5 ,r2-15r1
~
0 0 2 1 2 0 0 -1
0 0 -5 0 -14 1 -3 7
1 0 0 0 16/5 1/5 2/5 -13/5
0 1 0 0 -1 0 0 1 r2/-5，r1-2r2，交换行次序
~
1 0 0 0 16/5 1/5 2/5 -13/5
0 1 0 0 -1 0 0 1
0 0 1 0 14/5 -1/5 3/5 -7/5
0 0 0 1 -18/5 2/5 -6/5 9/5
得到E,A^-1，于是A的逆矩阵为
16/5 1/5 2/5 -13/5
-1 0 0 1
14/5 -1/5 3/5 -7/5
-18/5 2/5 -6/5 9/5
5、写出增广矩阵为
1 -2 1 -4
2 1 -3 7
-1 1 -1 2 r2-2r1,r3+r1
~
1 -2 1 -4
0 5 -5 15
0 -1 0 -2 r1-2r3，r2/5，r3+r2
~
1 0 1 0
0 1 -1 3
0 0 -1 1 r1+r3,r2-r3,r3*-1
~
1 0 0 1
0 1 0 2
0 0 1 -1
解得x1=1，x2=2，x3= -1
