Example TM Transpose of a $3\times 4$ matrix

Suppose \begin{equation*} D= \begin{bmatrix} 3&7&2&-3\\ -1&4&2&8\\ 0&3&-2&5 \end{bmatrix}. \end{equation*}

We could formulate the transpose, entry-by-entry, using the definition. But it is easier to just systematically rewrite rows as columns (or vice-versa). The form of the definition given will be more useful in proofs. So we have \begin{equation*} \transpose{D}= \begin{bmatrix} 3&-1&0\\ 7&4&3\\ 2&2&-2\\ -3&8&5 \end{bmatrix} \end{equation*}