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GATE 2022 CH – Question 12

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Given matrix $A = \begin{bmatrix} x & 1 & 3 \\ y & 2 & 6 \\ 3 & 5 & 7 \end{bmatrix}$, the ordered pair $(x, y)$ for which $\det(A) = 0$ is

  1. (1,1)
  2. (1,2)
  3. (2,2)
  4. (2,1)

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Correct answer: (B) (1,2)

Explanation

Expanding, $\det A = x(14 - 30) - 1(7y - 18) + 3(5y - 6) = -16x - 7y + 18 + 15y - 18 = 8y - 16x$. It is zero when $y = 2x$, which is the pair (1, 2).