Canonical URI: https://w3id.org/kmath/textbook_solution/chunjae_hong_solution_p157_p140_final_review_08
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 천재홍 p140 대단원 평가하기 8 풀이 |
| rdfs:comment | 천재홍 공통수학1 정답 및 풀이 p157의 p140 대단원 평가하기 8 풀이. |
| math:answerText | \(a=-\frac{1}{2}\) |
| math:explanationText | \[ AB=\begin{pmatrix}9&-1\\2&3\end{pmatrix} \begin{pmatrix}2&a\\1&-1\end{pmatrix} = \begin{pmatrix}17&9a+1\\7&2a-3\end{pmatrix} \] 이고 \[ BA=\begin{pmatrix}2&a\\1&-1\end{pmatrix} \begin{pmatrix}9&-1\\2&3\end{pmatrix} = \begin{pmatrix}18+2a&-2+3a\\7&-4\end{pmatrix}. \] \(AB=BA\)가 성립하려면 \(17=18+2a,\ 9a+1=-2+3a,\ 2a-3=-4\)이어야 하므로 \(a=-\frac{1}{2}\)이다. |
| math:mappingConfidence | 1.0 |
| math:pageStart | 157 |
| math:problem | textbook_problem:chunjae_hong_vision_p140_final_review_08 |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:matrix_equality_component_equations |
| math:usesSolutionPattern | solution_pattern:matrix_product_row_column |