大一线性代数第二题,用高斯消元法解该线性方程组,麻烦大家把过程写一下,我刚开始学还不太会,谢谢了。

2025-04-23 09:18:23
推荐回答(1个)
回答1:

A =
1 -2 3 -4 4
0 1 -1 1 -3
1 3 0 -3 1
0 -7 3 1 -3

A =
1 -2 3 -4 4
0 1 -1 1 -3
0 5 -3 1 -3
0 -7 3 1 -3

A =
1 -2 3 -4 4
0 1 -1 1 -3
0 0 2 -4 12
0 0 -4 8 -24

A =
1 -2 3 -4 4
0 1 -1 1 -3
0 0 2 -4 12
0 0 0 0 0

A =
1 -2 3 -4 4
0 1 -1 1 -3
0 0 1 -2 6
0 0 0 0 0

A =
1 -2 0 2 -14
0 1 0 -1 3
0 0 1 -2 6
0 0 0 0 0

A =
1 0 0 0 -8
0 1 0 -1 3
0 0 1 -2 6
0 0 0 0 0

所以:
x1 = -8
x2 = 3 + x4
x3 = 6 + 2x4
(x4为自由变量)