Question

find \\((0.6)a\\) for \\(a = \

$$\begin{bmatrix} -1 & 2 & 6 \\\\ 1 & 4 & 9 \\\\ 1 & 2 & 3 \\\\ -5 & 10 & -15 \\end{bmatrix}$$

\\).

\\(\circ\\) \\(\

$$\begin{bmatrix} -0.6 & 1.2 & 3.6 \\\\ 0.6 & 2.4 & 5.4 \\\\ 0.6 & 1.2 & 1.8 \\\\ -3 & 6 & -9 \\end{bmatrix}$$

\\)

\\(\circ\\) \\(\

$$\begin{bmatrix} -6 & 12 & 36 \\\\ 0.6 & 24 & 5.4 \\\\ 0.6 & 1.2 & 1.8 \\\\ -3 & 6 & -90 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
A =

$$\begin{bmatrix} -1 & 2 & -6 \\ 1 & 4 & 9 \\ 1 & 2 & 3 \\ -5 & 10 & -15 \end{bmatrix}$$

, \quad k = 0.6
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
(0.6)A =

$$\begin{bmatrix} 0.6 \cdot (-1) & 0.6 \cdot 2 & 0.6 \cdot 6 \\ 0.6 \cdot 1 & 0.6 \cdot 4 & 0.6 \cdot 9 \\ 0.6 \cdot 1 & 0.6 \cdot 2 & 0.6 \cdot 3 \\ 0.6 \cdot (-5) & 0.6 \cdot 10 & 0.6 \cdot (-15) \end{bmatrix}$$

\]

Simplify the resulting matrix elements

Using the Scalar Multiplication knowledge point
\[
(0.6)A =

$$\begin{bmatrix} -0.6 & 1.2 & 3.6 \\ 0.6 & 2.4 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -9 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -0.6 & 1.2 & 3.6 \\ 0.6 & 2.4 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -9 \end{bmatrix}$$

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

$$\begin{bmatrix} -6 & 12 & 36 \\ 0.6 & 24 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -90 \end{bmatrix}$$

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

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]
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</post_analysis>

Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
A =

$$\begin{bmatrix} -1 & 2 & -6 \\ 1 & 4 & 9 \\ 1 & 2 & 3 \\ -5 & 10 & -15 \end{bmatrix}$$

, \quad k = 0.6
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
(0.6)A =

$$\begin{bmatrix} 0.6 \cdot (-1) & 0.6 \cdot 2 & 0.6 \cdot 6 \\ 0.6 \cdot 1 & 0.6 \cdot 4 & 0.6 \cdot 9 \\ 0.6 \cdot 1 & 0.6 \cdot 2 & 0.6 \cdot 3 \\ 0.6 \cdot (-5) & 0.6 \cdot 10 & 0.6 \cdot (-15) \end{bmatrix}$$

\]

Simplify the resulting matrix elements

Using the Scalar Multiplication knowledge point
\[
(0.6)A =

$$\begin{bmatrix} -0.6 & 1.2 & 3.6 \\ 0.6 & 2.4 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -9 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -0.6 & 1.2 & 3.6 \\ 0.6 & 2.4 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -9 \end{bmatrix}$$

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

$$\begin{bmatrix} -6 & 12 & 36 \\ 0.6 & 24 & 5.4 \\ 0.6 & 1.2 & 1.8 \\ -3 & 6 & -90 \end{bmatrix}$$

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

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