Question

求线性方程组，要求详细过程。

问题如下，求大佬们助攻！

Answer 1

矩阵A=
3 -5 1 -2
2 3 -5 1
-1 7 -4 3
4 15 -7 9
=(r3与r1对调)
-1 7 -4 3
2 3 -5 1
3 -5 1 -2
4 15 -7 9
=(r2+2r1,r3+3r1,r4+4r1)
-1 7 -4 3
0 17 -13 7
0 16 -11 7
0 43 -23 21
=(r2-r3)
-1 7 -4 3
0 1 -2 0
0 16 -11 7
0 43 -23 21
=(r1-7r2,r4-3r3)
-1 0 10 3
0 1 -2 0
0 16 -11 7
0 -5 10 0
=(r3-16r2, -r1, -r4/5)
1 0 -10 -3
0 1 -2 0
0 0 21 7
0 1 -2 0
=(r3/7,r4-r2)
1 0 -10 -3
0 1 -2 0
0 0 3 1
0 0 0 0
等价于方程组
x1-10x3-3x4=0
x2-2x3=0
3x3+x4=0
解得
x1=k
x2=2k
x3=k
x4=-3k
即
解为
(x1,x2,x3,x4)^T=k(1,2,1,-3)^T

追答

k可以为任意数