Question

设矩阵A=(1 λ -1 2 ,2 -1 λ 5,1 10 -6 1),且R(A)=3,求λ.

Answer 1

1 λ -1 2

2 -1 λ 5

1 10 -6 1

->

1 λ -1 2

0 -1-2λ λ+2 1

0 10-λ -7 -1

->

1 λ -1 2

0 1 λ+2 -1-2λ

0 -1 -7 10-λ

->

1 λ -1 2

0 1 λ+2 -1-2λ

0 0 λ-5 9-3λ

->

1 0 0 0

0 1 0 0

0 0 λ-5 9-3λ

=>λ-5和9-3λ不同时为0

由于对任意λ都成立以上命题,故λ为任意值