Question

find \\(8a\\) for \\(a = \

$$\begin{bmatrix} -3 & 4 & 5 \\\\ 1 & -2 & 3 \\\\ 7 & 8 & 9 \\\\ -5 & 6 & -7 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -24 & 96 & 40 \\\\ 8 & -16 & 24 \\\\ 56 & 64 & 63 \\\\ -40 & 48 & -56 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -24 & 32 & 40 \\\\ 8 & -16 & 24 \\\\ 56 & 64 & 63 \\\\ -40 & 48 & -56 \\end{bmatrix}$$

\\)

Explanation:

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point

$$ A =
LATEXBLOCK0
, \quad k = 8 $$

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point

$$ 8A =
LATEXBLOCK1
=
LATEXBLOCK2
$$

Compare with the given options

The options visible in the image are:
Option 1:

$$
LATEXBLOCK3
$$

Option 2:

$$
LATEXBLOCK4
$$

Note: Both options in the image contain a typo in the third row, third column element, showing \(63\) instead of \(72\) (since \(8 \times 9 = 72\)). Comparing the two options, Option 2 correctly has \(32\) in the first row, second column (since \(8 \times 4 = 32\)), whereas Option 1 has \(96\). Therefore, Option 2 is the intended correct choice.

Answer:

• (A) \(

$$\begin{bmatrix} -24 & 96 & 40 \\ 8 & -16 & 24 \\ 56 & 64 & 63 \\ -40 & 48 & -56 \end{bmatrix}$$

\)

• **(B) \(

$$\begin{bmatrix} -24 & 32 & 40 \\ 8 & -16 & 24 \\ 56 & 64 & 63 \\ -40 & 48 & -56 \end{bmatrix}$$

\) (Correct answer)**