设矩阵 ,X为三阶矩阵，且满足矩阵方程AX+I=A²+X,求矩阵X.

A .https://assets.asklib.com/psource/2015103009171649882.jpg B .https://assets.asklib.com/psource/2015103009172871476.jpg C .https://assets.asklib.com/psource/2015103009173981959.jpg D .https://assets.asklib.com/psource/2015103009175260728.jpg

A . 无解 B . 只有零解 C . 有非零解 D . 不一定

A .https://assets.asklib.com/psource/60091447824735673.png B .https://assets.asklib.com/psource/36361447824745098.png C .https://assets.asklib.com/psource/78691447824753806.png D .https://assets.asklib.com/psource/63741448522749129.png

A. -2 B. -1/2 C. 1/2 D. 2

A．3 B．4 C．5 D．6 E．7

设m×n矩阵A的秩为R(A)-n-1， 且<img src='https://img2.soutiyun.com/ask/2020-12-17/977050765391984.png' />是齐次方程Ax=0的两个不同的解，则Ax=0的通解为() A.<img src='https://img2.soutiyun.com/ask/2020-12-17/977050784779092.png' /> B.<img src='https://img2.soutiyun.com/ask/2020-12-17/977050796368755.png' /> C.<img src='https://img2.soutiyun.com/ask/2020-12-17/977050810153544.png' /> D.<img src='https://img2.soutiyun.com/ask/2020-12-17/977050823541309.png' />

设矩阵，<img src='https://img2.soutiyun.com/ask/2020-08-12/966097576187859.png' />X为三阶矩阵，且满足矩阵方程AX+E=A²+X,求矩阵X.

设A=(a_ij)是m×n矩阵，β=(b₁，b₂，···，b_n)是n维行向量，如果方程组(I)Ax=0的解全是方程(II)b₁x₁+b₂x₂+···+b_nx_n=0)的解，证明β可用A的行向量α₁，α₂，···，α_m线性表出。

设A是m×n阶矩阵，下列命题正确的是()． A．若方程组AX=0只有零解，则方程组AX＝b有唯一解 B．若方程组AX=0有非零解，则方程组AX＝b有无穷多个解 C．若方程组AX＝b无解，则方程组Ax＝0一定有非零解 D．若方程组AX＝b有无穷多个解，则方程组AX＝0一定有非零解

A．AX=b必有无穷多解 B．AX=b必有唯一解 C．AX=0必有唯一解 D．AX=0必有非零解

设A为<img src='https://img2.soutiyun.com//1/2021-05-24/990704515439966.jpg' />矩阵,且方程组Ax=0的基础解系含有两个解向量,则秩(A)=()

设三阶实对称矩阵A的特征值<img src='https://img2.soutiyun.com/ask/2020-12-29/978123429410498.png' />是A属于<img src='https://img2.soutiyun.com/ask/2020-12-29/978122670425087.png' />1的一个特征向量，记<img src='https://img2.soutiyun.com/ask/2020-12-29/978123455698002.png' />其中E为三阶单位矩阵。 (1)验证口是矩阵B的特征向量，并求B的全部特征值与特征向量 (2)求矩阵B

A．1 B．-1 C．2 D．-2

设矩阵<img src='https://img2.soutiyun.com/ask/2021-03-04/983717526085576.png' />且满足AX+E=A²+X.其中E是3阶单位矩阵,求X.