用高斯消元法解下列线性代数方程组
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/31 20:59:42
用高斯消元法解下列线性代数方程组
X1+2X2-X3-2X4=2
2X1-X2+X3-2X4=3
X1-2X2+X4=-5
X1+2X2-X3-2X4=2
2X1-X2+X3-2X4=3
X1-2X2+X4=-5
增广矩阵 =
1 2 -1 -2 2
2 -1 1 -2 3
1 -2 0 1 -5
r1+r2
3 1 0 -4 5
2 -1 1 -2 3
1 -2 0 1 -5
r2+r1,r3+2r1
3 1 0 -4 5
5 0 1 -6 8
7 0 0 -7 5
r3*(1/7),r1-3r3,r2-5r3
0 1 0 -1 20/7
0 0 1 -1 31/7
1 0 0 -1 5/7
交换行
1 0 0 -1 5/7
0 1 0 -1 20/7
0 0 1 -1 31/7
方程组的通解为:(5/7,20/7,31/7,0)^T + c(1,1,1,1)^T.
1 2 -1 -2 2
2 -1 1 -2 3
1 -2 0 1 -5
r1+r2
3 1 0 -4 5
2 -1 1 -2 3
1 -2 0 1 -5
r2+r1,r3+2r1
3 1 0 -4 5
5 0 1 -6 8
7 0 0 -7 5
r3*(1/7),r1-3r3,r2-5r3
0 1 0 -1 20/7
0 0 1 -1 31/7
1 0 0 -1 5/7
交换行
1 0 0 -1 5/7
0 1 0 -1 20/7
0 0 1 -1 31/7
方程组的通解为:(5/7,20/7,31/7,0)^T + c(1,1,1,1)^T.