Question

let $d = \

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

$, $e = \

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

$

a student performs the matrix operation $3e + d$. select the correct matrix the student should get as a result

$\circ \

$$\begin{bmatrix} 21 & 4 \\\\ 8 & 7 \\end{bmatrix}$$

$

$\circ \

$$\begin{bmatrix} 21 & 0 \\\\ 6 & 15 \\end{bmatrix}$$

$

$\circ \

$$\begin{bmatrix} 7 & -4 \\\\ 0 & 13 \\end{bmatrix}$$

$

Explanation:

Step1: Calculate 3E

To find \( 3E \), we multiply each element of matrix \( E \) by 3. Given \( E =

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

\), we have:
\[
3E = 3 \times

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

=

$$\begin{bmatrix} 3\times0 & 3\times(-2) \\ 3\times(-1) & 3\times4 \end{bmatrix}$$

=

$$\begin{bmatrix} 0 & -6 \\ -3 & 12 \end{bmatrix}$$

\]

Step2: Add matrix D to 3E

Now, we add matrix \( D =

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

\) to \( 3E \). To add two matrices, we add their corresponding elements:
\[
3E + D =

$$\begin{bmatrix} 0 + 7 & -6 + 2 \\ -3 + 3 & 12 + 1 \end{bmatrix}$$

=

$$\begin{bmatrix} 7 & -4 \\ 0 & 13 \end{bmatrix}$$

\]

Answer:

\(

$$\begin{bmatrix} 7 & -4 \\ 0 & 13 \end{bmatrix}$$

\) (the third option)