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}\

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}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Matrix Scalar Multiplication", "Matrix Addition" ], "current_concepts": [ "Matrix Scalar Multiplication", "Matrix Addition" ] } ## 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 $$ -21A + B = \begin{bmatrix} -235 & 158 & -333 \ -397 & 306 & -256 \end{bmatrix} $$ $$ -21A + B = \begin{bmatrix} -235 & 158 & -333 \ -397 & 306 & -256 \end{bmatrix} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Matrix Addition" ] }

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Question

Explanation:

Calculate the scalar multiplication \(-21A\)

Add matrix B to \(-21A\)

Simplify the resulting matrix elements

Answer: