The Transpose

Practice Questions

Linear Algebra › The Transpose

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1

Find the transpose of Matrix .

$A=\begin{bmatrix} 1& 4\ 5& 8 \end{bmatrix}$

2

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

3

$\begin{align*}&\text{Find the transpose of }A=\begin{bmatrix}-15&3\-2&18\end{bmatrix}\end{align*}$

4

is a two-by-two matrix such that

$A + A^{T} = \begin{bmatrix} -10& 0\ 0& 16 \end{bmatrix}$

Which of the following could be?

5

$\begin{align*}&\text{Find the transpose of }\begin{bmatrix}1&2\-2&-6\-8&-20\-18&-14\16&15\20&3\end{bmatrix}^{T}\end{align*}$

6

Let and be any two matrices of the same dimensions.

True or false:

It must hold that $(A+B)^{T} = A^{T}+ B^{T}$ .

7

$A = \begin{bmatrix} 3 & 0 & -3 \ 6& 0 & 9 \end{bmatrix}$

Which of the following is equal to $A^{T}$ ?

8

Which is the transpose of $\begin{bmatrix} 1 &8 & 4\2 &-3 &0 \end{bmatrix}$ ?

9

$A^{*} = \begin{bmatrix} 3 + i & 5 - 2i \3 + 2i & 3i \end{bmatrix}$

Which of the following is equal to $A^{T}$ ?

10

Find the transpose of matrix A.

$A=\begin{bmatrix} 7&4 \ 2&8 \ 1&3 \end{bmatrix}$

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