Question:
If $\begin{bmatrix} a & 2 & 3 \\ b & 5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ -1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 13 \\ 12 & 11 \end{bmatrix}$, then $(a, b)$ is}
If $\begin{bmatrix} a & 2 & 3 \\ b & 5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ -1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 13 \\ 12 & 11 \end{bmatrix}$, then $(a, b)$ is}
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Matrix multiplication: $(AB)_{ij} = \sum_k A_{ik}B_{kj}$. Solve for unknowns by equating specific entries of the product to the given matrix.
Updated On: May 2, 2026
- $(1, -2)$
- $(-1, -4)$
- $(1, 3)$
- $(1, -4)$
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Perform matrix multiplication row by column and equate to the given result.
Step 2: Detailed Explanation:
Row 1, col 1: $a(1)+2(3)+3(-1) = a+3 = 4 \Rightarrow a = 1$.
Row 2, col 1: $b(1)+5(3)+(-1)(-1) = b+16 = 12 \Rightarrow b = -4$.
Step 3: Final Answer:
$(a, b) = (1, -4)$.
Perform matrix multiplication row by column and equate to the given result.
Step 2: Detailed Explanation:
Row 1, col 1: $a(1)+2(3)+3(-1) = a+3 = 4 \Rightarrow a = 1$.
Row 2, col 1: $b(1)+5(3)+(-1)(-1) = b+16 = 12 \Rightarrow b = -4$.
Step 3: Final Answer:
$(a, b) = (1, -4)$.
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