当λ为何值时,方程组(1+λ)x1+x2+x3=1x1+(1+λ)x2+x3=λ有唯一解x1+x2+(1+λ)x3=λ2

Question

当λ为何值时,方程组(1+λ)x1+x2+x3=1 x1+(1+λ)x2+x3=λ有唯一解 x1+x2+(1+λ)x3=λ2

Answer 1

方程组(1+λ)x1+x2+x3=1,
x1+(1+λ)x2+x3=λ
x1+x2+(1+λ)x3=λ^2有唯一解,行列式
|1+λ 1 1|
|1 1+λ 1|
|1 1 1+λ|=
|λ -λ 0|
|0 λ -λ|
|1 1 1+λ|=
|λ 0 0|
|0 λ -λ|
|1 2 1+λ|=λ^2*(3+λ)≠0,
∴λ≠0或-3.