求方程组：x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4

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求方程组：x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4
(2) X1-4x2+2x3-3x4=11
4x1+3x2+6x3-x4=-1
2x1+4x2+2x3+x4=-6

(1) 增广矩阵 =
1 1 -1 2 3
2 1 0 -3 1
-2 0 -2 10 4
r3+r2,r2-2r1
1 1 -1 2 3
0 -1 2 -7 -5
0 1 -2 7 5
r1+r2,r3+r2,r2*(-1)
1 0 1 -5 -2
0 1 -2 7 5
0 0 0 0 0
方程组的通解为:(-2,5,0,0)^T+c1(-1,2,1,0)^T+c2(5,-7,0,1)^T.
(2)
增广矩阵 =
1 -4 2 -3 11
4 3 6 -1 -1
2 4 2 1 -6
r2-4r1,r3-2r1
1 -4 2 -3 11
0 19 -2 11 -45
0 12 -2 7 -28
r2-r3
1 -4 2 -3 11
0 7 0 4 -17
0 12 -2 7 -28
r2*(1/7),r1+4r2,r3-12r2
1 0 2 -5/7 9/7
0 1 0 4/7 -17/7
0 0 -2 1/7 8/7
r1+r3,r3*(-1/2)
1 0 0 -4/7 17/7
0 1 0 4/7 -17/7
0 0 1 -1/14 -4/7
方程组的通解为:(17/7,-17/7,-4/7,0)^T + c(8,-8,1,14)^T.

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