.解线性方程组｜X1+X2+X3+X4=5 ｜X1+2X2-X3+4X4=-2 ｜2X1-3X2-X3-5X4=-2 ｜3X1+X2+2X3+11X4=0

题目

.解线性方程组｜X1+X2+X3+X4=5 ｜X1+2X2-X3+4X4=-2 ｜2X1-3X2-X3-5X4=-2 ｜3X1+X2+2X3+11X4=0

答案

增广矩阵=
1 1 1 1 5
1 2 -1 4 -2
2 -3 -1 -5 -2
3 1 2 11 0
用初等行变换化为
1 0 0 0 1
0 1 0 0 2
0 0 1 0 3
0 0 0 1 -1
方程组有唯一解:(1,2,3,-1)^T.