齐次线性方程组kx+y+z=0x+ky-z=02x-y+z=0有非零解,则系数k必须满足

Question

齐次线性方程组 kx+y+z=0 x+ky-z=0 2x-y+z=0 有非零解,则系数k必须满足

Answer 1

齐次线性方程组 kx+y+z=0 x+ky-z=0 2x-y+z=0 有非零解,
所以
系数行列式=0
即
|k 1 1
1 k -1
2 -1 1|
=|k 1 1
1+k k+1 0
2-k -2 0|
=|1+k k+1
2-k -2 |
=(k+1)*
| 1 1
2-k -2|
=(k+1)(k-4)=0
k=-1或k=4