Answer:
a) [tex]\sf \begin{bmatrix} 3 & 5 \\ 4 & 8 \end{bmatrix}[/tex]
Step-by-step explanation:
The transpose of a matrix is an operation that flips a matrix over its diagonal, switching its rows with its columns.
Given the matrix:
[tex]\sf A = \begin{bmatrix} 3 & 4 \\ 5 & 8 \end{bmatrix} [/tex]
The transpose of [tex]\bold{ A }[/tex], denoted as [tex]\bold{ A^T }[/tex], is calculated by rearranging its elements such that the rows become columns and vice versa:
[tex]\sf A^T = \begin{bmatrix} 3 & 5 \\ 4 & 8 \end{bmatrix} [/tex]
Therefore, the transpose of the given matrix [tex]\bold{ A }[/tex] is:
[tex]\sf \begin{bmatrix} 3 & 5 \\ 4 & 8 \end{bmatrix}[/tex]
In summary, transposing a matrix involves reflecting its elements over its main diagonal, resulting in a new matrix where rows become columns and columns become rows.
