Question

解含有参数的线性方程组 2x1-x2+5x3+px4=5 x1-x2+2x3+3x4=4 4x1-3x2+9x3+8x4

Answer 1

增广矩阵 =

2 -1 5 p 5

1 -1 2 3 4

4 -3 9 8 q

r1-2r2,r3-4r2

0 1 1 p-6 -3

1 -1 2 3 4

0 1 1 -4 q-16

r3-r1,r2+r1

0 1 1 p-6 -3

1 0 3 p-3 1

0 0 0 2-p q-13

由已知条件,p=2,q=13.

增广矩阵化为

1 0 3 -1 1

0 1 1 -4 -3

0 0 0 0 0

方程组的通解为:(1,-3,0,0)'+c1(3,1,-1,0)'+c2(1,4,0,1)'.