用矩阵的初等变换解下列线性方程组x1+2x2+x3=3-2x1+x2-x3=-3x1-4x2+2x3=-5

Question

用矩阵的初等变换解下列线性方程组x1+2x2+x3=3 -2x1+x2-x3=-3 x1-4x2+2x3=-5

Answer 1

1 2 1 3
-2 1 -1 -3
1 -4 2 -5
r2+2r1,r3-r1
1 2 1 3
0 5 1 3
0 -6 1 -8
r2+r3
1 2 1 3
0 -1 2 -5
0 -6 1 -8
r1+2r2,r3-6r2,r2*(-1)
1 0 5 -7
0 1 -2 5
0 0 -11 22
r3*(-1/11),r1-5r3,r2+2r3
1 0 0 3
0 1 0 1
0 0 1 -2
方程组有唯一解 (3,1,-2)^T