求齐次线性 (1)A-8B+10C+2D=0 2A+4B+5C-D=0 3A+8B+6C-2D=0 (2) A+B=5
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求齐次线性 (1)A-8B+10C+2D=0 2A+4B+5C-D=0 3A+8B+6C-2D=0 (2) A+B=5 2A+B+C+2D=1 5a+3B+2C+2D=3?
(1) 解: 系数矩阵 =
1 -8 10 2
2 4 5 -1
3 8 6 -2
r3-r1-r2, r2-2r1
1 -8 10 2
0 20 -15 -5
0 12 -9 -3
r2*(1/20)
1 -8 10 2
0 1 -3/4 -1/4
0 12 -9 -3
r1+8r2,r4-12r2
1 0 4 0
0 1 -3/4 -1/4
0 0 0 0
方程组的通解为: c1(-4, 3/4,1,0)'+c2(0,1/4,0,1)'.
(2)解: 增广矩阵 =
1 1 0 0 5
2 1 1 2 1
5 3 2 2 3
r3-r1-2r2, r2-2r1
1 1 0 0 5
0 -1 1 2 -9
0 0 0 -2 -4
r2+r3,r1+r2, r2*(-1),r3*(-1/2)
1 0 1 0 -8
0 1 -1 0 13
0 0 0 1 2
方程组的通解为 (-8,13,0,2)'+c1(1,-1,-1,0)'.
1 -8 10 2
2 4 5 -1
3 8 6 -2
r3-r1-r2, r2-2r1
1 -8 10 2
0 20 -15 -5
0 12 -9 -3
r2*(1/20)
1 -8 10 2
0 1 -3/4 -1/4
0 12 -9 -3
r1+8r2,r4-12r2
1 0 4 0
0 1 -3/4 -1/4
0 0 0 0
方程组的通解为: c1(-4, 3/4,1,0)'+c2(0,1/4,0,1)'.
(2)解: 增广矩阵 =
1 1 0 0 5
2 1 1 2 1
5 3 2 2 3
r3-r1-2r2, r2-2r1
1 1 0 0 5
0 -1 1 2 -9
0 0 0 -2 -4
r2+r3,r1+r2, r2*(-1),r3*(-1/2)
1 0 1 0 -8
0 1 -1 0 13
0 0 0 1 2
方程组的通解为 (-8,13,0,2)'+c1(1,-1,-1,0)'.
求齐次线性 (1)A-8B+10C+2D=0 2A+4B+5C-D=0 3A+8B+6C-2D=0 (2) A+B=5
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