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Mathematics Question on Matrices

Find the transpose of each of the following matrices:
I.[512−1]\begin{bmatrix}5\\\\\frac{1}{2}\\\\-1\end {bmatrix}

II.[1−1\23]\begin{bmatrix}1&-1\\\2&3\end{bmatrix}

III.[−156356\23−1]\begin{bmatrix}-1&5&6\\\\\sqrt3&5&6\\\2&3&-1\end{bmatrix}

Answer

(i) Let A=[512−1]\begin{bmatrix}5\\\\\frac{1}{2}\\\\-1\end {bmatrix}

then A-T= [512−1]\begin{bmatrix}5&\frac{1}{2}&-1\end{bmatrix}

(ii)Let A= [1−1\23]\begin{bmatrix}1&-1\\\2&3\end{bmatrix}

then A-T= [12−13]\begin{bmatrix}1&2\\\\-1&3\end{bmatrix}

(iii)Let A= [−156356\23−1]\begin{bmatrix}-1&5&6\\\\\sqrt3&5&6\\\2&3&-1\end{bmatrix}

then A-T = [−132\553\66−1]\begin{bmatrix}-1&\sqrt3&2\\\5&5&3\\\6&6&-1\end{bmatrix}