Question

question 2 points 3

find \\(-8n\\) if \\(n = \

$$\begin{bmatrix} 1 & -1 & 2 & -2 & -3 \\\\ 3 & -4 & 4 & -5 & 5 \\\\ 6 & -6 & 7 & -7 & 8 \\\\ -8 & 9 & -9 & 0 & 10 \\\\ -10 & -20 & 20 & -30 & 30 \\end{bmatrix}$$

\\).

\\(\bigcirc\\) \\(\

$$\begin{bmatrix} 8 & -8 & 16 & -16 & -24 \\\\ 24 & -32 & 32 & -40 & 40 \\\\ 48 & -48 & 56 & -56 & 64 \\\\ -64 & 72 & -72 & 0 & 80 \\\\ -80 & -160 & 160 & -240 & 240 \\end{bmatrix}$$

\\)

\\(\bigcirc\\) \\(\

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

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
N =

$$\begin{bmatrix} 1 & -1 & 2 & -2 & -3 \\ 3 & -4 & 4 & -5 & 5 \\ 6 & -6 & 7 & -7 & 8 \\ -8 & 9 & -9 & 0 & 10 \\ -10 & -20 & 20 & -30 & 30 \end{bmatrix}$$

, \quad k = -8
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-8N =

$$\begin{bmatrix} -8(1) & -8(-1) & -8(2) & -8(-2) & -8(-3) \\ -8(3) & -8(-4) & -8(4) & -8(-5) & -8(5) \\ -8(6) & -8(-6) & -8(7) & -8(-7) & -8(8) \\ -8(-8) & -8(9) & -8(-9) & -8(0) & -8(10) \\ -8(-10) & -8(-20) & -8(20) & -8(-30) & -8(30) \end{bmatrix}$$

\]

Simplify the resulting matrix elements

Using the Scalar Multiplication knowledge point
\[
-8N =

$$\begin{bmatrix} -8 & 8 & -16 & 16 & 24 \\ -24 & 32 & -32 & 40 & -40 \\ -48 & 48 & -56 & 56 & -64 \\ 64 & -72 & 72 & 0 & -80 \\ 80 & 160 & -160 & 240 & -240 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 8 & -8 & 16 & -16 & -24 \\ 24 & -32 & 32 & -40 & 40 \\ 48 & -48 & 56 & -56 & 64 \\ -64 & 72 & -72 & 0 & 80 \\ -80 & -160 & 160 & -240 & 240 \end{bmatrix}$$

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

$$\begin{bmatrix} -8 & 8 & -16 & 16 & 24 \\ -24 & 32 & -32 & 40 & -40 \\ -48 & 48 & -56 & 56 & -64 \\ 64 & -72 & 72 & 0 & -80 \\ 80 & 160 & -160 & 240 & -240 \end{bmatrix}$$

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

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Scalar Multiplication"
]
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</post_analysis>

Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
N =

$$\begin{bmatrix} 1 & -1 & 2 & -2 & -3 \\ 3 & -4 & 4 & -5 & 5 \\ 6 & -6 & 7 & -7 & 8 \\ -8 & 9 & -9 & 0 & 10 \\ -10 & -20 & 20 & -30 & 30 \end{bmatrix}$$

, \quad k = -8
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-8N =

$$\begin{bmatrix} -8(1) & -8(-1) & -8(2) & -8(-2) & -8(-3) \\ -8(3) & -8(-4) & -8(4) & -8(-5) & -8(5) \\ -8(6) & -8(-6) & -8(7) & -8(-7) & -8(8) \\ -8(-8) & -8(9) & -8(-9) & -8(0) & -8(10) \\ -8(-10) & -8(-20) & -8(20) & -8(-30) & -8(30) \end{bmatrix}$$

\]

Simplify the resulting matrix elements

Using the Scalar Multiplication knowledge point
\[
-8N =

$$\begin{bmatrix} -8 & 8 & -16 & 16 & 24 \\ -24 & 32 & -32 & 40 & -40 \\ -48 & 48 & -56 & 56 & -64 \\ 64 & -72 & 72 & 0 & -80 \\ 80 & 160 & -160 & 240 & -240 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 8 & -8 & 16 & -16 & -24 \\ 24 & -32 & 32 & -40 & 40 \\ 48 & -48 & 56 & -56 & 64 \\ -64 & 72 & -72 & 0 & 80 \\ -80 & -160 & 160 & -240 & 240 \end{bmatrix}$$

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

$$\begin{bmatrix} -8 & 8 & -16 & 16 & 24 \\ -24 & 32 & -32 & 40 & -40 \\ -48 & 48 & -56 & 56 & -64 \\ 64 & -72 & 72 & 0 & -80 \\ 80 & 160 & -160 & 240 & -240 \end{bmatrix}$$

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

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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
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