已知向量组I: (alpha )_(1)=((1,1,4))^T, (alpha )_(2)=((1,0,4))^T, _(3)=((1,2,{a)^2+3)}^rI: (alpha )_(1)=((1,1,4))^T, (alpha )_(2)=((1,0,4))^T, _(3)=((1,2,{a)^2+3)}^r若向量组Ⅰ与向量组Ⅱ等价,求a的取值,并将β3用α1, α2, α3线性表示。

(本题满分11分)

已知向量组

若向量组Ⅰ与向量组Ⅱ等价,求a的取值,并将β3用α1, α2, α3线性表示。

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