Question

求下列方程组的全部解

Answer 1

写出增广矩阵为
2 -1 -1 1 -3 4
-3 2 -5 -4 1 -1
1 -1 2 -1 3 -4

-4 1 3 -9 16 -21 r4+2r1,r1-2r3,r2+3r3
~
0 1 -5 3 -9 12
0 -1 1 -7 10 -13
1 -1 2 -1 3 -4

0 -1 1 -7 10 -13 r4-r2,r2+r1,r3+r1
~
0 1 -5 3 -9 12
0 0 -4 -4 1 -1
1 0 -3 2 -6 8
0 0 0 0 0 r2/-4,r1+5r2,r3+3r2，交换行次序
~
1 0 0 5 -27/4 35/4
0 1 0 8 -41/4 53/4
0 0 1 1 -1/4 1/4
0 0 0 0 0

于是得到方程组的解为y=c1(-5,-8,-1,1,0)^T+c2(27,41,1,0,4)^T+(35/4,53/4,1/4,0,0)^T
c1c2为常数