确定a,b的值使下列线性方程组有解,并求其解 题目见补充：

(1) 增广矩阵 =
2 -1 1 1 1
1 2 -1 1 2
1 7 -4 11 a
r1-2r2, r3-r2
0 -5 3 -1 -3
1 2 -1 1 2
0 5 -3 10 a-2
r3+r1
0 -5 3 -1 -3
1 2 -1 1 2
0 0 0 9 a-5
r1*(-1/5), r3*(1/9)
0 1 -3/5 1/5 3/5
1 2 -1 1 2
0 0 0 1 a/9-5/9
r1+(1/5)r3, r2-r3
0 1 -3/5 0 32/45 - a/45
1 2 -1 0 23/9 - a/9
0 0 0 1 a/9 - 5/9
r2-2r1
0 1 -3/5 0 32/45 - a/45
1 0 1/5 0 17/45 - a/45
0 0 0 1 a/9 - 5/9
a 取任何值方程组都有解
通解为: (17/45 - a/45, 32/45 - a/45, 0, a/9 - 5/9)' + c(-1/5,3/5,1,0)'
(2)
1 2 -2 2 2
0 1 -1 -1 1
1 1 -1 3 a
1 -1 1 5 b
r3-r1,r4-r1
1 2 -2 2 2
0 1 -1 -1 1
0 -1 1 1 a-2
0 -3 3 3 b-2
r1-2r2, r3+r2, r4+3r2
1 0 0 4 0
0 1 -1 -1 1
0 0 0 0 a-1
0 0 0 0 b+1
当a=1,b=-1 时方程组有解,
通解为 (0,1,0,0)'+c1(0,1,1,0)'+c2(-4,1,0,1)'.
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