Operations and Properties

Practice Questions

Linear Algebra › Operations and Properties

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1

Determine the inverse of matrix A where

$A=\begin{bmatrix} 2&-8 \ 1&4 \end{bmatrix}$

2

$\begin{align*}&\text{Conclude whether or not the matrix }A=\begin{bmatrix}-0.60587&0.79556\0.79556&0.60587\end{bmatrix}\&\text{is orthogonal.}\end{align*}$

3

Assume M is an orthogonal matrix. Which of the following is not always true?

4

is an unitary matrix.

True or false: $A^{2}$ must be an unitary matrix.

5

and are square matrices of the same dimension.

True or false: $\textup{Tr}(A) + \textup{Tr}(B) = \textup{Tr}(A+B)$

6

Find the norm of the vector $\vec{v} = (4, 3, 0)$

7

Calculate the trace.

$\begin{bmatrix} 1&4 \ 5&-1 \end{bmatrix}$

8

$\begin{align*}&\text{Determine the trace of the matrix}\&A=\begin{bmatrix}-8&-7\-3&0\end{bmatrix}\end{align*}$

9

True or false: The transpose of a matrix with six rows and seven columns has seven rows and six columns.

10

Consider the matrix

$A = \begin{bmatrix} 2& 3& -1\ -2& 1& 0\ 0& 1& 2 \end{bmatrix}$

Calculate the cofactor $C_{2,1}$ of this matrix.

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