【例19】(2025-2)设矩阵A=(alpha_(1),alpha_(2),alpha_(3),alpha_(4)).若alpha_(1),alpha_(2),alpha_(3)线性无关，且alpha_(1)+alpha_(2)=alpha_(3)+alpha_(4)，则方程组AX=alpha_(1)+4alpha_(4)的通解为X=____.

【例19】(2025-2)设矩阵$A=(\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4})$.若$\alpha_{1},\alpha_{2},\alpha_{3}$线性无关，且$\alpha_{1}+\alpha_{2}=\alpha_{3}+\alpha_{4}$，则方程组$AX=\alpha_{1}+4\alpha_{4}$的通解为X=____.

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