Question

question 14 points 2

if \\( b = \

$$\begin{bmatrix} 2 & 3 & -4 \\\\ 4 & 5 & 6 \\\\ 6 & 0 & 8 \\end{bmatrix}$$

\\), then find \\( -3b \\).

\\( \bigcirc \

$$\begin{bmatrix} 2 & 3 & -4 \\\\ 4 & 5 & 6 \\\\ 6 & 0 & 8 \\end{bmatrix}$$

\\)

\\( \bigcirc \

$$\begin{bmatrix} -6 & -9 & 12 \\\\ -12 & -15 & -18 \\\\ -18 & 0 & -24 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
B =

$$\begin{bmatrix} 2 & 3 & -4 \\ 4 & 5 & 6 \\ 6 & 0 & 8 \end{bmatrix}$$

, \quad k = -3
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-3B =

$$\begin{bmatrix} -3(2) & -3(3) & -3(-4) \\ -3(4) & -3(5) & -3(6) \\ -3(6) & -3(0) & -3(8) \end{bmatrix}$$

=

$$\begin{bmatrix} -6 & -9 & 12 \\ -12 & -15 & -18 \\ -18 & 0 & -24 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(

$$\begin{bmatrix} 2 & 3 & -4 \\ 4 & 5 & 6 \\ 6 & 0 & 8 \end{bmatrix}$$

\)</mcq-option>
<mcq-correct>(B) \(

$$\begin{bmatrix} -6 & -9 & 12 \\ -12 & -15 & -18 \\ -18 & 0 & -24 \end{bmatrix}$$

\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
B =

$$\begin{bmatrix} 2 & 3 & -4 \\ 4 & 5 & 6 \\ 6 & 0 & 8 \end{bmatrix}$$

, \quad k = -3
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-3B =

$$\begin{bmatrix} -3(2) & -3(3) & -3(-4) \\ -3(4) & -3(5) & -3(6) \\ -3(6) & -3(0) & -3(8) \end{bmatrix}$$

=

$$\begin{bmatrix} -6 & -9 & 12 \\ -12 & -15 & -18 \\ -18 & 0 & -24 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(

$$\begin{bmatrix} 2 & 3 & -4 \\ 4 & 5 & 6 \\ 6 & 0 & 8 \end{bmatrix}$$

\)</mcq-option>
<mcq-correct>(B) \(

$$\begin{bmatrix} -6 & -9 & 12 \\ -12 & -15 & -18 \\ -18 & 0 & -24 \end{bmatrix}$$

\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Scalar Multiplication"
]
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