Question - Matrix Transpose Determination
Solution:
To find $$ A^T $$, which is the transpose of the given matrix $$ A $$, you need to swap the rows of $$ A $$ with its columns. The matrix $$ A $$ is:\[ A = \begin{bmatrix} 5 & 1 \\ 2 & 3 \\ -1 & 4 \end{bmatrix} \]So the transpose of this matrix, denoted $$ A^T $$, where each row of $$ A $$ becomes a column, will be:\[ A^T = \begin{bmatrix} 5 & 2 & -1 \\ 1 & 3 & 4 \end{bmatrix} \]Matching this with the options provided:A. \[ \begin{bmatrix} 5 & 1 \\ 2 & 3 \\ 1 & 4 \end{bmatrix} \] (incorrect)B. \[ \begin{bmatrix} 5 & 2 & -1 \\ 1 & 3 & 4 \end{bmatrix} \] (correct)C. \[ \begin{bmatrix} -5 & -2 & -3 \\ 1 & -4 \end{bmatrix} \] (incorrect)D. Nothing above (incorrect)The correct answer is option B.
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