Find the transpose of each of the following matrices

Question

Question:

Find the transpose of each of the following matrices:

A =$~~\left[ \begin{matrix} 0 \ 1 \ -2 \ \end{matrix} ight]$

B =$~\left[ \begin{matrix} 5 & 1 & -6 \ \end{matrix} ight]$

C =$~\left[ \begin{matrix} 1 & 2 \ 2 & -1 \ 3 & 0 \ \end{matrix} ight]$

D = $\left[ \begin{matrix} 2 & 3 \ 0 & 5 \ \end{matrix} ight]$

E = $\left[ \begin{matrix} 2 & 3 \ -4 & 5 \ \end{matrix} ight]$

F = $\left[ \begin{matrix} 1 & 2 \ 3 & 4 \ \end{matrix} ight]$

Accepted Answer

Solution:

Transpose of a matrix is obtained by converting all the columns of that matrix to the rows and all the rows to the columns. So, according to the definition

(i) $ m{A}^{t}$ =$~~\left[ \begin{matrix} 0 & 1 & -2 \ \end{matrix} ight]$

(ii) $ m{B}^{t}$ =$~\left[ \begin{matrix} 5 \ 1 \ -6 \ \end{matrix} ight]$

(iii) $ m{C}^{t}$ =$~~$ $\left[ \begin{matrix} 1 & 2 & 3 \ 2 & -1 & 0 \ \end{matrix} ight]$

(iv) $ m{D}^{t}$ = $\left[ \begin{matrix} 2 & 0 \ 3 & 5 \ \end{matrix} ight]$

(v) $ m{E}^{t}$ = $\left[ \begin{matrix} 2 & -4 \ 3 & 5 \ \end{matrix} ight]$

(vi) $ m{F}^{t}$ = $\left[ \begin{matrix} 1 & 3 \ 2 & 4 \ \end{matrix} ight]$