Question

find \\(8n\\) for the given matrix.
\\(n = \

$$\begin{bmatrix} 2 & 5 & 18 & 6 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} 16 & 40 & 144 & 48 \\end{bmatrix}$$

\\)
\\(\bigcirc \

$$\begin{bmatrix} -16 & 40 & -144 & 48 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[

$$\begin{aligned} &N = \begin{bmatrix} 2 & 5 & 18 & 6 \end{bmatrix}\\ &k = 8 \end{aligned}$$

\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[

$$\begin{aligned} 8N &= 8 \begin{bmatrix} 2 & 5 & 18 & 6 \end{bmatrix}\\ &= \begin{bmatrix} 8 \cdot 2 & 8 \cdot 5 & 8 \cdot 18 & 8 \cdot 6 \end{bmatrix}\\ &= \begin{bmatrix} 16 & 40 & 144 & 48 \end{bmatrix} \end{aligned}$$

\]
</reasoning>

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

$$\begin{bmatrix} 16 & 40 & 144 & 48 \end{bmatrix}$$

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

$$\begin{bmatrix} -16 & 40 & -144 & 48 \end{bmatrix}$$

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

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Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[

$$\begin{aligned} &N = \begin{bmatrix} 2 & 5 & 18 & 6 \end{bmatrix}\\ &k = 8 \end{aligned}$$

\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[

$$\begin{aligned} 8N &= 8 \begin{bmatrix} 2 & 5 & 18 & 6 \end{bmatrix}\\ &= \begin{bmatrix} 8 \cdot 2 & 8 \cdot 5 & 8 \cdot 18 & 8 \cdot 6 \end{bmatrix}\\ &= \begin{bmatrix} 16 & 40 & 144 & 48 \end{bmatrix} \end{aligned}$$

\]
</reasoning>

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

$$\begin{bmatrix} 16 & 40 & 144 & 48 \end{bmatrix}$$

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

$$\begin{bmatrix} -16 & 40 & -144 & 48 \end{bmatrix}$$

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

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