Question

determina

1. \\(-21 a + b\\)

\\a = \

$$\begin{bmatrix} 12 & -7 & 15 \\\\ 18 & 14 & 13 \\end{bmatrix}$$

\\

\\b = \

$$\begin{bmatrix} 17 & 11 & -18 \\\\ -19 & 12 & 17 \\end{bmatrix}$$

\\

\\c = \

$$\begin{bmatrix} -27 & 19 & -14 \\\\ 14 & 12 & -29 \\end{bmatrix}$$

\\

Explanation:

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"Matrix Addition"
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<reasoning>

Calculate the scalar multiplication \(-21A\)

\[
A =

$$\begin{bmatrix} 12 & -7 & 15 \\ 18 & -14 & 13 \end{bmatrix}$$

\]
\[
-21A =

$$\begin{bmatrix} -21 \times 12 & -21 \times (-7) & -21 \times 15 \\ -21 \times 18 & -21 \times (-14) & -21 \times 13 \end{bmatrix}$$

=

$$\begin{bmatrix} -252 & 147 & -315 \\ -378 & 294 & -273 \end{bmatrix}$$

\]

Add matrix B to \(-21A\)

\[
B =

$$\begin{bmatrix} 17 & 11 & -18 \\ -19 & 12 & 17 \end{bmatrix}$$

\]
\[
-21A + B =

$$\begin{bmatrix} -252 + 17 & 147 + 11 & -315 + (-18) \\ -378 + (-19) & 294 + 12 & -273 + 17 \end{bmatrix}$$

\]

Simplify the resulting matrix elements

\[
-21A + B =

$$\begin{bmatrix} -235 & 158 & -333 \\ -397 & 306 & -256 \end{bmatrix}$$

\]
</reasoning>

<answer>
\[
-21A + B =

$$\begin{bmatrix} -235 & 158 & -333 \\ -397 & 306 & -256 \end{bmatrix}$$

\]
</answer>

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"subject": "Mathematics",
"question_type": "Free Response",
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"Mathematics",
"Algebra",
"Matrix Addition"
]
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</post_analysis>

Answer:

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],
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"Matrix Scalar Multiplication",
"Matrix Addition"
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</pre_analysis>

<reasoning>

Calculate the scalar multiplication \(-21A\)

\[
A =

$$\begin{bmatrix} 12 & -7 & 15 \\ 18 & -14 & 13 \end{bmatrix}$$

\]
\[
-21A =

$$\begin{bmatrix} -21 \times 12 & -21 \times (-7) & -21 \times 15 \\ -21 \times 18 & -21 \times (-14) & -21 \times 13 \end{bmatrix}$$

=

$$\begin{bmatrix} -252 & 147 & -315 \\ -378 & 294 & -273 \end{bmatrix}$$

\]

Add matrix B to \(-21A\)

\[
B =

$$\begin{bmatrix} 17 & 11 & -18 \\ -19 & 12 & 17 \end{bmatrix}$$

\]
\[
-21A + B =

$$\begin{bmatrix} -252 + 17 & 147 + 11 & -315 + (-18) \\ -378 + (-19) & 294 + 12 & -273 + 17 \end{bmatrix}$$

\]

Simplify the resulting matrix elements

\[
-21A + B =

$$\begin{bmatrix} -235 & 158 & -333 \\ -397 & 306 & -256 \end{bmatrix}$$

\]
</reasoning>

<answer>
\[
-21A + B =

$$\begin{bmatrix} -235 & 158 & -333 \\ -397 & 306 & -256 \end{bmatrix}$$

\]
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Matrix Addition"
]
}
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