a_(m)),证明向量组(I)线性相关当且仅当m元齐次线性方程组Ax=0有非零解.<|im_end|>4. 已知alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，证明：alpha_(1)+alpha_(2),alpha_(2)+alpha_(3),alpha_(3)+alpha_(4),alpha_(4)-alpha_(1)线性无关.<|im_end|>5.设行列式D=}2&1&4&1-1&2&0&61&2&3&25&0&6&2证明3A_(21)-A_(22)+2A_(23)+A_(24)=0和3M_(12)-M_(22)+2M_(32)+M_(42)=-62.

1.设A为n阶对称矩阵，B为n阶反对称矩阵. 证明：(1)$AB-BA$为对称矩阵；(2)$AB+BA$为反对称矩阵. <|im_end|> 2.设n阶矩阵A的伴随矩阵为$A^{*}$，证明： (1)若$|A|=0$，则$|A^{*}|=0$； (2)$|A^{*}|=|A|^{n-1}$. <|im_end|> 3.设n维向量组(I):$a_{1},a_{2},\cdots,a_{m}$,矩阵$A=(a_{1} a_{2} \cdots a_{m})$,证明向量组(I)线性相关当且仅当m元齐次线性方程组Ax=0有非零解. <|im_end|> 4. 已知$\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}$线性无关，证明：$\alpha_{1}+\alpha_{2},\alpha_{2}+\alpha_{3},\alpha_{3}+\alpha_{4},\alpha_{4}-\alpha_{1}$线性无关. <|im_end|> 5.设行列式 $D=\begin{vmatrix}2&1&4&1\\-1&2&0&6\\1&2&3&2\\5&0&6&2\end{vmatrix}$ 证明$3A_{21}-A_{22}+2A_{23}+A_{24}=0$和$3M_{12}-M_{22}+2M_{32}+M_{42}=-62$.

参考答案与解析：

相关试题

设alpha_(1),alpha_(2),alpha_(3)是四元非齐次线性方程组Ax=b的三个解向量，且A的秩R: 设alpha_(1),alpha_(2),alpha_(3)是四元非齐次线性方程组Ax=b的三个解向量，且A的秩R 设$\alpha_{1},\alpha_{

查看答案

例9 设alpha_(1),alpha_(2),alpha_(3)是四元非齐次线性方程组Ax=b的3个解向量，且秩r(A)=3.alpha_(1)=(1,2,3,4)^T,alpha_(2)+alph: 例9 设alpha_(1),alpha_(2),alpha_(3)是四元非齐次线性方程组Ax=b的3个解向量，且秩r(A)=3.alpha_(1)=(1,2,3

查看答案

8、填空设alpha_(1),alpha_(2)是 3times 3非齐次线性方程组Ax=b的两个不同的解向量，已知A=(}1&-1&22&0&: 8、填空设alpha_(1),alpha_(2)是 3times 3非齐次线性方程组Ax=b的两个不同的解向量，已知A=(}1&-1&22&a

查看答案

设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alpha_(4),beta线性相关，则下列命题: 设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alph

查看答案

设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alpha_(4),beta线性相关，则下列命题: 设alpha_(1),alpha_(2),alpha_(3),alpha_(4)线性无关，且alpha_(1),alpha_(2),alpha_(3),alph

查看答案

设alpha_(1), alpha_(2), alpha_(3)是三元非齐线性方程组Ax = b的三个互不相同的解，且R: 设alpha_(1), alpha_(2), alpha_(3)是三元非齐线性方程组Ax = b的三个互不相同的解，且R 设$\alpha_{1}, \alp

查看答案

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

查看答案

4.判断题向量β被向量组alpha_(1),alpha_(2),...,alpha_(n)线性表示，记A=[alpha_(1),alpha_(2),...,alpha_(n)]，则Ax=β可能无解。: 4.判断题向量β被向量组alpha_(1),alpha_(2),...,alpha_(n)线性表示，记A=[alpha_(1),alpha_(2),...,al

查看答案

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

查看答案

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_(2),alpha_(3)线性表示。证: 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

查看答案

参考答案与解析：

相关试题