question 29 points 1

consider $i = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $b = \begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$. find $ib$.

- $b$
- $i$
- cannot be determined
- all of the choices

Question

question 29 points 1

consider $i = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $b = \begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$. find $ib$.

- $b$
- $i$
- cannot be determined
- all of the choices

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Matrix Multiplication" ], "new_concepts": [], "current_concepts": [ "Matrix Multiplication", "Identity Matrix" ] } ## Identify the given matrices Using the *Matrix Multiplication* knowledge point $$ I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 10 \ 6 & 5 \end{bmatrix} $$ ## Compute the matrix product Using the *Matrix Multiplication* knowledge point $$ IB = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 2 & 10 \ 6 & 5 \end{bmatrix} = \begin{bmatrix} 1(2) + 0(6) & 1(10) + 0(5) \ 0(2) + 1(6) & 0(10) + 1(5) \end{bmatrix} = \begin{bmatrix} 2 & 10 \ 6 & 5 \end{bmatrix} = B $$

(A) $B$

(B) $I$

(C) Cannot be determined

(D) All of the choices

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Matrix Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given matrices

Compute the matrix product

Answer: