GATE AG 2013 • Q1
MCQ • 1 Mark
Section 1: Engineering Mathematics
Linear Algebra
Subtopic: Matrices and determinants
Question Statement:
If $P = A \times B$, where $A = \begin{bmatrix} 2 & 1 \\ 3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 0 \\ 2 & 1 & 2 \end{bmatrix}$, then $P$ is
Options:
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(A) $\begin{bmatrix} 7 & 2 \\ 9 & 0 \end{bmatrix}$
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(B) $\begin{bmatrix} 4 & 7 & 2 \\ 3 & 9 & 0 \end{bmatrix}$
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(C) $\begin{bmatrix} 2 & 4 \\ 3 & 9 \end{bmatrix}$
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(D) $\begin{bmatrix} 2 & 4 & 7 \\ 0 & 3 & 9 \end{bmatrix}$
Step-by-Step Solution & Explanation
Standard matrix multiplication, P = A×B (2×2 times 2×3 gives 2×3):
Row 1: [2×1+1×2, 2×3+1×1, 2×0+1×2] = [4, 7, 2]
Row 2: [3×1+0×2, 3×3+0×1, 3×0+0×2] = [3, 9, 0]
P = [[4,7,2],[3,9,0]]. Answer: (B). (Verified symbolically.)
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