1. find the determinant for the matrix:

\\begin{bmatrix} 4 & -6 \\ 2 & 3 \end{bmatrix}\

Question

1. find the determinant for the matrix:

\\begin{bmatrix} 4 & -6 \\ 2 & 3 \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 Determinant", "2x2 Determinant" ], "current_concepts": [ "Matrix Determinant", "2x2 Determinant" ] } ## Identify the matrix elements $$ A = \begin{bmatrix} 4 & -6 \ 2 & 3 \end{bmatrix} $$ ## Apply the determinant formula $$ \det(A) = ad - bc $$ $$ \det(A) = (4)(3) - (-6)(2) $$ ## Calculate the final value $$ \det(A) = 12 - (-12) = 12 + 12 = 24 $$ 24 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Matrix Determinant" ] }

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Question

Explanation:

Identify the matrix elements

Apply the determinant formula

Calculate the final value

Answer: