GATE AG 2015 • Q12 MCQ • 1 Mark

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

Inverse of the matrix $\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$ is

Options:

  • (A) $\begin{bmatrix} 0.1 & -0.4 \\ -0.3 & 0.2 \end{bmatrix}$
  • (B) $\begin{bmatrix} 0.3 & -0.2 \\ -0.1 & 0.4 \end{bmatrix}$
  • (C) $\begin{bmatrix} 0.3 & -0.1 \\ -0.2 & 0.4 \end{bmatrix}$
  • (D) $\begin{bmatrix} 0.4 & -0.2 \\ -0.1 & 0.3 \end{bmatrix}$

Official Answer Key:

D

Step-by-Step Solution & Explanation

For A = [[3,2],[1,4]], determinant = (3×4) − (2×1) = 12 − 2 = 10. A⁻¹ = (1/det)×[[d,−b],[−c,a]] = (1/10)×[[4,−2],[−1,3]] = [[0.4, −0.2], [−0.1, 0.3]]. This matches option (D) exactly. The other options result from common sign or transposition slips when applying the 2×2 inverse formula. Hence (D) is correct.

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