4.求向量组alpha_(1)=(1,1,2,3),alpha_(2)=(1,-1,1,1),alpha_(3)=(1,3,3,5),alpha_(4)=(4,-2,5,6),alpha_(5)=(3,1,5,7)的一个极大无关组，并将其余向量用该极大无关组线性表示.

已知向量组alpha_(1),alpha_(2),alpha_(3)线性无关，若alpha_(1)+alpha_(2),alpha_(2)+alpha_(3),

设向量组alpha_(1)=(1,-1,2,4),alpha_(2)=(0,3,1,2),alpha_(3)=(3,0,7,14),alpha_(4)=(1,-

4.(判断题) 向量组满足 beta_(1)=alpha_(1), beta_(2)=alpha_(1)+alpha_(2), beta_(3)=alpha_(

7.设alpha_(1),alpha_(2),alpha_(3),beta_(1),beta_(2)均为4维列向量，矩阵A=(alpha_(1),alpha_(

设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alph

设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alph

8.求向量组 alpha_(1)=(1,-1,5,-1)^T, alpha_(2)=(1,1,-2,3)^T, alpha_(3)=(3,-1,8,1)^T,

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

【例19】(2025-2)设矩阵A=(alpha_(1),alpha_(2),alpha_(3),alpha_(4)).若alpha_(1),alpha_(2)

3.判断题设向量beta可由向量组alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性表示，但不能由alpha_(1),alpha