Question

question 6 points 2

calculate \\(-2b\\) if \\(b = \

$$\begin{bmatrix} 1.5 & 3 \\\\ 2.5 & 4 \\\\ -1 & 4.5 \\end{bmatrix}$$

\\).

\\(\bigcirc \

$$\begin{bmatrix} 3 & 6 \\\\ 5 & 8 \\\\ -2 & 9 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -3 & -6 \\\\ -5 & -8 \\\\ 2 & -9 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
B =

$$\begin{bmatrix} 1.5 & 3 \\ 2.5 & 4 \\ -1 & 4.5 \end{bmatrix}$$

, \quad k = -2
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-2B =

$$\begin{bmatrix} -2(1.5) & -2(3) \\ -2(2.5) & -2(4) \\ -2(-1) & -2(4.5) \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & -6 \\ -5 & -8 \\ 2 & -9 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

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

$$\begin{bmatrix} -3 & -6 \\ -5 & -8 \\ 2 & -9 \end{bmatrix}$$

\)</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 =

$$\begin{bmatrix} 1.5 & 3 \\ 2.5 & 4 \\ -1 & 4.5 \end{bmatrix}$$

, \quad k = -2
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
-2B =

$$\begin{bmatrix} -2(1.5) & -2(3) \\ -2(2.5) & -2(4) \\ -2(-1) & -2(4.5) \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & -6 \\ -5 & -8 \\ 2 & -9 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

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

$$\begin{bmatrix} -3 & -6 \\ -5 & -8 \\ 2 & -9 \end{bmatrix}$$

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

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