求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解

题目

求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解

答案

增广矩阵 =
1 -3 -2 -1 1
3 -8 -4 -1 0
-2 1 -4 2 1
-1 -2 -6 1 2
r2-3r1,r3+2r1,r4+r1
1 -3 -2 -1 1
0 1 2 2 -3
0 -5 -8 0 3
0 -5 -8 0 3
r4-r3,r3+5r2,r1+3r2
1 0 4 5 -8
0 1 2 2 -3
0 0 2 10 -12
0 0 0 0 0
r1-2r3,r2-r3,r3*(1/2)
1 0 0 -15 16
0 1 0 -8 9
0 0 1 5 -6
0 0 0 0 0
方程组的解为:(16,9,-6,0)'+c(15,8,-5,1)'.