求解线性方程组：2X1+3X3=1 x1-X2+2x3=1 X1-3X2+4X3=2
2019-05-07
求解线性方程组：2X1+3X3=1 x1-X2+2x3=1 X1-3X2+4X3=2
优质解答
解: 增广矩阵 =
2 0 3 1
1 -1 2 1
1 -3 4 2
r1-2r2,r3-r2
0 2 -1 -1
1 -1 2 1
0 -2 2 1
r1+r3, r3*(-1/2), r2+r3
0 0 1 0
1 0 1 1/2
0 1 -1 -1/2
r2-r1,r3+r1
0 0 1 0
1 0 0 1/2
0 1 0 -1/2
交换行
1 0 0 1/2
0 1 0 -1/2
0 0 1 0
方程组的解为: (1/2,-1/2,0)'.
解: 增广矩阵 =
2 0 3 1
1 -1 2 1
1 -3 4 2
r1-2r2,r3-r2
0 2 -1 -1
1 -1 2 1
0 -2 2 1
r1+r3, r3*(-1/2), r2+r3
0 0 1 0
1 0 1 1/2
0 1 -1 -1/2
r2-r1,r3+r1
0 0 1 0
1 0 0 1/2
0 1 0 -1/2
交换行
1 0 0 1/2
0 1 0 -1/2
0 0 1 0
方程组的解为: (1/2,-1/2,0)'.