线代测试题及详细答案.docx

线代测试题及详细答案

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一、选择题（每题2分，共10分）

1.设矩阵\(A=\begin{bmatrix}12\\34\end{bmatrix}\)，则\(A\)的伴随矩阵\(A^*\)是：

A.\(\begin{bmatrix}2-1\\-31\end{bmatrix}\)

B.\(\begin{bmatrix}-21\\3-1\end{bmatrix}\)

C.\(\begin{bmatrix}4-2\\-31\end{bmatrix}\)

D.\(\begin{bmatrix}-42\\3-1\end{bmatrix}\)

2.设向量\(\vec{a}=\begin{bmatrix}1\\2\end{bmatrix}\)，\(\vec{b}=\begin{bmatrix}2\\3\end{bmatrix}\)，则\(\vec{a}\)与\(\vec{b}\)的点积是：

A.7

B.5

C.1

D.-1

3.若\(A\)为\(n\)阶可逆矩阵，则\(A^{-1}A\)的行列式值为：

A.1

B.0

C.\(n\)

D.不确定

4.设\(A\)为\(n\)阶实对称矩阵，则\(A\)必定是：

A.正定矩阵

B.非负定矩阵

C.非正定矩阵

D.以上都不对

5.已知\(A=\begin{bmatrix}11\\11\end{bmatrix}\)，则\(A\)的特征值为：

A.2

B.1

C.0

D.1和2

二、填空题（每题2分，共10分）

6.若向量\(\vec{a}\)与\(\vec{b}\)正交，则\(\vec{a}\cdot\vec{b}=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_