Question

consider matrices c and d.$c = \begin{bmatrix} 1 & 4 & -8 \\ 3 & -5 & 2 end{bmatrix}$, $d = \begin{bmatrix} 13 & 2 & -5 \\ 6 & -4 & 0 end{bmatrix}$which matrix is the result of subtracting matrix c from matrix d?$circ \begin{bmatrix} 12 & -2 & 3 \\ 3 & 1 & -2 end{bmatrix}$$circ \begin{bmatrix} 14 & 6 & -13 \\ 9 & -9 & 2 end{bmatrix}$$circ \begin{bmatrix} 14 & 2 & 3 \\ 3 & 1 & 2 end{bmatrix}$$circ \begin{bmatrix} 12 & -2 & -13 \\ 3 & -9 & -2 end{bmatrix}$

Explanation:

Step1: Define matrix subtraction

To find $D - C$, subtract corresponding elements.

Step2: Calculate row 1 elements

$$\begin{align*} 13-1&=12\\ 2-4&=-2\\ -5-(-8)&=3 \end{align*}$$

Step3: Calculate row 2 elements

$$\begin{align*} 6-3&=3\\ -4-(-5)&=1\\ 0-2&=-2 \end{align*}$$

Step4: Form result matrix

Combine the calculated elements into a matrix.

Answer:

$$\begin{bmatrix}12 & -2 & 3\\3 & 1 & -2\end{bmatrix}$$

(the first option)