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}

• A. $(1, -2)$
• B. $(-1, -4)$
• C. $(1, 3)$
• D. $(1, -4)$

Hint:

Matrix multiplication: $(AB)_{ij} = \sum_k A_{ik}B_{kj}$. Solve for unknowns by equating specific entries of the product to the given matrix.

Answer 1

The Correct Option is D

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:
$(a, b) = (1, -4)$.