Answer :

Answer:

[tex] \binom{3 \: \: \: 5}{4 \: \: \: \: 8} [/tex]

Step-by-step explanation:

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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.