Question

question 8 points 2

calculate -k for the matrix \\( k = \

$$\begin{bmatrix} 3 & -8 \\\\ 4 & -6 \\\\ 10 & 8 \\end{bmatrix}$$

\\).

\\( \bigcirc \

$$\begin{bmatrix} -3 & 8 \\\\ -4 & 6 \\\\ -10 & -8 \\end{bmatrix}$$

\\)

\\( \bigcirc \

$$\begin{bmatrix} 8 & 3 \\\\ 6 & 4 \\\\ 8 & 10 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Define the given matrix

Using the Matrix Negation knowledge point
\[
k =

$$\begin{bmatrix} 3 & -8 \\ 4 & -6 \\ 10 & 8 \end{bmatrix}$$

\]

Apply scalar multiplication

Using the Scalar Multiplication knowledge point
\[
-k = -1 \cdot

$$\begin{bmatrix} 3 & -8 \\ 4 & -6 \\ 10 & 8 \end{bmatrix}$$

=

$$\begin{bmatrix} -1 \cdot 3 & -1 \cdot (-8) \\ -1 \cdot 4 & -1 \cdot (-6) \\ -1 \cdot 10 & -1 \cdot 8 \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & 8 \\ -4 & 6 \\ -10 & -8 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} -3 & 8 \\ -4 & 6 \\ -10 & -8 \end{bmatrix}$$

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

$$\begin{bmatrix} 8 & 3 \\ 6 & 4 \\ 8 & 10 \end{bmatrix}$$

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

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"Mathematics",
"Algebra",
"Matrix Negation"
]
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</post_analysis>

Answer:

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<reasoning>

Define the given matrix

Using the Matrix Negation knowledge point
\[
k =

$$\begin{bmatrix} 3 & -8 \\ 4 & -6 \\ 10 & 8 \end{bmatrix}$$

\]

Apply scalar multiplication

Using the Scalar Multiplication knowledge point
\[
-k = -1 \cdot

$$\begin{bmatrix} 3 & -8 \\ 4 & -6 \\ 10 & 8 \end{bmatrix}$$

=

$$\begin{bmatrix} -1 \cdot 3 & -1 \cdot (-8) \\ -1 \cdot 4 & -1 \cdot (-6) \\ -1 \cdot 10 & -1 \cdot 8 \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & 8 \\ -4 & 6 \\ -10 & -8 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} -3 & 8 \\ -4 & 6 \\ -10 & -8 \end{bmatrix}$$

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

$$\begin{bmatrix} 8 & 3 \\ 6 & 4 \\ 8 & 10 \end{bmatrix}$$

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

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Matrix Negation"
]
}
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