Question

select the correct answer.
consider matrices a, b, c, and d:
$a = \

$$\begin{bmatrix}-1&4\\\\5&-2\\\\3&4\\end{bmatrix}$$

$, $b = \

$$\begin{bmatrix}4&4\\\\4&4\\\\4&4\\end{bmatrix}$$

$, $c = \

$$\begin{bmatrix}-1&2&5\\\\0&-4&1\\\\-4&3&1\\end{bmatrix}$$

$, $d = \

$$\begin{bmatrix}3&6&-9\\\\1&4&2\\\\3&-5&0\\end{bmatrix}$$

$
what is the sum of the two square matrices?
a. $\

$$\begin{bmatrix}2&8&4\\\\-1&0&-3\\\\7&8&10\\end{bmatrix}$$

$
b. $\

$$\begin{bmatrix}3&8\\\\9&2\\\\7&8\\end{bmatrix}$$

$
c. $\

$$\begin{bmatrix}3&6&5\\\\4&0&1\\\\0&7&1\\end{bmatrix}$$

$
d. $\

$$\begin{bmatrix}2&8&-4\\\\1&0&3\\\\-1&-2&1\\end{bmatrix}$$

$

Explanation:

Step1: Identify square matrices

A square matrix has equal rows and columns.

• $A$: $3 \times 2$ (not square)
• $B$: $2 \times 2$ (square)
• $C$: $3 \times 3$ (square)
• $D$: $3 \times 3$ (square)

Only $C$ and $D$ are same-order square matrices (3x3), so we sum them.

Step2: Sum corresponding elements

Add each pair of elements from $C$ and $D$:

$$ C + D =
LATEXBLOCK0
$$

Step3: Calculate each element

Simplify each entry:

$$ C + D =
LATEXBLOCK1
$$

Answer:

D.

$$\begin{bmatrix} 2 & 8 & -4 \\ 1 & 0 & 3 \\ -1 & -2 & 1 \end{bmatrix}$$