Find the transpose of each of the following matrices :

(i) $\left[ {\begin{array}{cccccccccccccccccccc}5\\{\cfrac{1}{2}}\\{ - 1}\end{array}} \right]$

(ii) $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\2&3\end{array}} \right]$

(iii) $\left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&5&6\\{\sqrt 3 }&5&6\\2&3&{ - 1}\end{array}} \right]$

.:

(i) Transpose of $\left[ {\begin{array}{cccccccccccccccccccc}5\\{\cfrac{1}{2}}\\{ - 1}\end{array}} \right]$

%$= {\left[ {\begin{array}{cccccccccccccccccccc}5\\{\cfrac{1}{2}}\\{ - 1}\end{array}} \right]^{\prime}}$

$= \left[ {\begin{array}{cccccccccccccccccccc}5&{\cfrac{1}{2}}&{ - 1}\end{array}} \right]$

(ii) Transpose of $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\2&3\end{array}} \right]$

% $= {\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\2&3\end{array}} \right]^{\prime}}$

$= \left[ {\begin{array}{cccccccccccccccccccc}1&2\\{ - 1}&3\end{array}} \right]$

(iii) Transpose of $\left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&5&6\\{\sqrt 3 }&5&6\\2&3&{ - 1}\end{array}} \right]$

% $= {\left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&5&6\\{\sqrt 3 }&5&6\\2&3&{ - 1}\end{array}} \right]^{\prime}}$

$= \left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&{\sqrt 3 }&2\\5&5&3\\6&6&{ - 1}\end{array}} \right]$