Question - Matrix Transpose Calculation
Solution:
The image is asking to find the transpose of a given matrix $$ A $$. The transpose of a matrix is obtained by swapping its rows with columns. For the given matrix\[ A = \begin{pmatrix} 5 & 2 & -1 \\ 1 & 3 & 4 \end{pmatrix} \]The transpose, denoted by $$ A^T $$, would be\[ A^T = \begin{pmatrix} 5 & 1 \\ 2 & 3 \\ -1 & 4 \end{pmatrix} \]So, the elements of the first row of $$ A $$ become the elements of the first column of $$ A^T $$, the elements of the second row of $$ A $$ become the elements of the second column of $$ A^T $$, and so forth.
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