Question

Evaluate the following matrix multiplication: \[ 5 \times \begin{pmatrix} 5 & 7 \\ 6 & 8 \end{pmatrix} \]

• A. \(\begin{pmatrix} 25 & 35 \\ 30 & 8 \end{pmatrix}\)
• B. \(\begin{pmatrix} 25 & 35 \\ 30 & 40 \end{pmatrix}\)
• C. \(\begin{pmatrix} 5 & 35 \\ 6 & 40 \end{pmatrix}\)
• D. \(\begin{pmatrix} 25 & 25 \\ 30 & 40 \end{pmatrix}\)

Hint:

When multiplying a matrix by a scalar, simply multiply each element of the matrix by that scalar. This operation is straightforward and doesn't require additional steps.

Answer 1

The Correct Option is B

We are given the matrix: \[ 5 \times \begin{pmatrix} 5 & 7
6 & 8 \end{pmatrix} \] To multiply a scalar (5) with a matrix, simply multiply each element of the matrix by 5: \[ 5 \times \begin{pmatrix} 5 & 7
6 & 8 \end{pmatrix} = \begin{pmatrix} 5 \times 5 & 5 \times 7
5 \times 6 & 5 \times 8 \end{pmatrix} = \begin{pmatrix} 25 & 35
30 & 40 \end{pmatrix} \] Thus, the result is \(\begin{pmatrix} 25 & 35
30 & 40 \end{pmatrix}\).