Question:
Find the transpose of each of the following matrices:
Difficulty: Easy
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) $\rm{A}^{t}$ =$~~\left[ \begin{matrix} 0 & 1 & -2 \\ \end{matrix} \right]$
(ii) $\rm{B}^{t}$ =$~\left[ \begin{matrix} 5 \\ 1 \\ -6 \\ \end{matrix} \right]$
(iii) $\rm{C}^{t}$ =$~~$ $\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & -1 & 0 \\ \end{matrix} \right]$
(iv) $\rm{D}^{t}$ = $\left[ \begin{matrix} 2 & 0 \\ 3 & 5 \\ \end{matrix} \right]$
(v) $\rm{E}^{t}$ = $\left[ \begin{matrix} 2 & -4 \\ 3 & 5 \\ \end{matrix} \right]$
(vi) $\rm{F}^{t}$ = $\left[ \begin{matrix} 1 & 3 \\ 2 & 4 \\ \end{matrix} \right]$
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