Question

X1—3X2+2X3=0 2X1—5x2+3x3=0 3x1—8x2+TX3=0 t=?齐次矩阵求通解

Answer 1

系数矩阵A=

1 -3 2

2 -5 3

3 -8 t

r2-2r1,r3-3r1

1 -3 2

0 1 -1

0 1 t-6

r1+3r2,r3-r2

1 0 -1

0 1 -1

0 0 t-5

当t≠5时,方程组只有零解

当t=5时

A-->

1 0 -1

0 1 -1

0 0 0

方程组的通解为 k(1,1,1)^T.