Question

complete the following matrix operation using matrices d and e let $d = \

$$\begin{bmatrix}7 & 2 \\\\ 3 & 1\\end{bmatrix}$$

$, $e = \

$$\begin{bmatrix}0 & -2 \\\\ -1 & 4\\end{bmatrix}$$

$
4d

Explanation:

Step1: Recall scalar multiplication of matrix

To multiply a matrix by a scalar, we multiply each element of the matrix by the scalar. Given matrix \( D =

$$\begin{bmatrix}7&2\\3&1\end{bmatrix}$$

\) and scalar \( 4 \), we need to multiply each element of \( D \) by \( 4 \).

Step2: Multiply each element by 4

For the first element in the first row: \( 4\times7 = 28 \)
For the second element in the first row: \( 4\times2 = 8 \)
For the first element in the second row: \( 4\times3 = 12 \)
For the second element in the second row: \( 4\times1 = 4 \)

So, \( 4D=

$$\begin{bmatrix}4\times7&4\times2\\4\times3&4\times1\end{bmatrix}$$

=

$$\begin{bmatrix}28&8\\12&4\end{bmatrix}$$

\)

Answer:

\(

$$\begin{bmatrix}28&8\\12&4\end{bmatrix}$$

\)