Mashaal Masha

Question:

 

Find the transpose of each of the following matrices:

 

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

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

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

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

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

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

 

 

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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