已知向量组alpha_(1),alpha_(2),alpha_(3)线性无关，证明：alpha_(1)+2alpha_(2),2alpha_(1)+3alpha_(3),3alpha_(3)+alpha_(1)线性无关。

已知向量组$\alpha_{1},\alpha_{2},\alpha_{3}$线性无关，证明：$\alpha_{1}+2\alpha_{2},2\alpha_{1}+3\alpha_{3},3\alpha_{3}+\alpha_{1}$线性无关。

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