非齐次线性方程组X1-5X2+2X3-3X4=11 5X1+3X2+6X3-X4=-1 2X1+4X2+2X3+X4=-6用导出组的基础解系表示通解

求详细解答
2024-12-20 04:00:23
推荐回答(1个)
回答1:

增广矩阵 =
1 -5 2 -3 11
5 3 6 -1 -1
2 4 2 1 -6

r2-5r1, r3-2r1
1 -5 2 -3 11
0 28 -4 14 -56
0 14 -2 7 -28

r2-2r3, r3*(1/14)
1 -5 2 -3 11
0 0 0 0 0
0 1 -1/7 1/2 -2

r1+5r3
1 0 9/7 -1/2 1
0 0 0 0 0
0 1 -1/7 1/2 -2

所以通解为: (1,-2,0,0)'+c1(-9,1,7,0)'+c2(1,-1,0,2), c1,c2 为任意常数.

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