Find the transpose of each of the following matrices:

Question:

Find the transpose of each of the following matrices:

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

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

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

Solution:

(i) Let $A=\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$, then $A^{\mathrm{T}}=\left[\begin{array}{lll}5 & \frac{1}{2} & -1\end{array}\right]$

(ii) Let $A=\left[\begin{array}{rr}1 & -1 \\ 2 & 3\end{array}\right]$, then $A^{\mathrm{T}}=\left[\begin{array}{rr}1 & 2 \\ -1 & 3\end{array}\right]$

(iii) Let $A=\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$, then $A^{\mathrm{T}}=\left[\begin{array}{ccc}-1 & \sqrt{3} & 2 \\ 5 & 5 & 3 \\ 6 & 6 & -1\end{array}\right]$

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