Question

which of the following matrices is equal to $2\

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

-\

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

=$?
\\(\circ\\) \\(\

$$\begin{bmatrix}11&-5\\\\6&-2\\end{bmatrix}$$

\\)
\\(\circ\\) \\(\

$$\begin{bmatrix}14&-2\\\\2&-26\\end{bmatrix}$$

\\)
\\(\circ\\) \\(\

$$\begin{bmatrix}5&-3\\\\6&-2\\end{bmatrix}$$

\\)
\\(\circ\\) \\(\

$$\begin{bmatrix}11&-3\\\\6&-18\\end{bmatrix}$$

\\)
\\(\circ\\) \\(\

$$\begin{bmatrix}5&-5\\\\6&-18\\end{bmatrix}$$

\\)

Explanation:

Step1: Multiply the first matrix by 2

To multiply a matrix by a scalar, we multiply each element of the matrix by the scalar. For the matrix \(

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

\), multiplying by 2 gives:

$$ 2
LATEXBLOCK1
=
LATEXBLOCK2
=
LATEXBLOCK3
$$

Step2: Subtract the second matrix

Now we subtract the matrix \(

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

\) from the result of Step 1. To subtract two matrices, we subtract the corresponding elements. So:

$$
LATEXBLOCK5
-
LATEXBLOCK6
=
LATEXBLOCK7
=
LATEXBLOCK8
=
LATEXBLOCK9
$$

Answer:

\(

$$\begin{bmatrix}11&-3\\6&-18\end{bmatrix}$$

\) (the fourth option in the given choices)