用矩阵的初等行变换解下列线性方程组X1-3X2+7X3=202X1+4X2-3X3=-1-3X1+7X2+2X3=7

Question

用矩阵的初等行变换解下列线性方程组
X1-3X2+7X3=20
2X1+4X2-3X3=-1
-3X1+7X2+2X3=7

Answer 1

增广矩阵=
1 -3 7 20
2 4 -3 -1
-3 7 2 7
r3+r1+r2, r2-2r1
1 -3 7 20
0 10 -17 -41
0 8 6 26
r2-r3
1 -3 7 20
0 2 -23 -67
0 8 6 26
r3-4r2
1 -3 7 20
0 2 -23 -67
0 0 98 294
r3*(1/98)
1 -3 7 20
0 2 -23 -67
0 0 1 3
r1-7r3,r2+23r3
1 -3 0 -1
0 2 0 2
0 0 1 3
r2*(1/2),r1+3r2
1 0 0 2
0 1 0 1
0 0 1 3
方程组有唯一解 (2,1,3)^T