a1=(λ+3,λ,3λ+3)T,a2=(1,1—λ,λ)T,a3=(2,1,λ+3)T问λ取何值时,向量组线性相关
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a1=(λ+3,λ,3λ+3)T,a2=(1,1—λ,λ)T,a3=(2,1,λ+3)T问λ取何值时,向量组线性相关
![a1=(λ+3,λ,3λ+3)T,a2=(1,1—λ,λ)T,a3=(2,1,λ+3)T问λ取何值时,向量组线性相关](/uploads/image/z/3201355-19-5.jpg?t=a1%3D%28%CE%BB%2B3%2C%CE%BB%2C3%CE%BB%2B3%29T%2Ca2%3D%281%2C1%E2%80%94%CE%BB%2C%CE%BB%29T%2Ca3%3D%282%2C1%2C%CE%BB%2B3%29T%E9%97%AE%CE%BB%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%2C%E5%90%91%E9%87%8F%E7%BB%84%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3)
矩阵的行列式为
|a1 a2 a3|
=(λ+3)(1-λ)(λ+3)+(3λ+3)+2λ^2-2(3λ+3)(1-λ)-λ(λ+3)-λ(λ+3)
= -λ^3+λ^2-6λ+6
= -(λ-1)(λ^2+6) ,
所以 λ=1 时,向量组线性相关 .
|a1 a2 a3|
=(λ+3)(1-λ)(λ+3)+(3λ+3)+2λ^2-2(3λ+3)(1-λ)-λ(λ+3)-λ(λ+3)
= -λ^3+λ^2-6λ+6
= -(λ-1)(λ^2+6) ,
所以 λ=1 时,向量组线性相关 .
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