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GATE 2024 BT – Question 28

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

A value of $k$ for which the linear equations $(k-1)x + 3y = 0$ and $2x + ky = 0$ have a non-zero solution is ________.

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (C) 3

Explanation

The determinant must be zero: $k(k-1) - 6 = 0$, so $k^2 - k - 6 = 0$ and $k = 3$ or $k = -2$. Only 3 is listed.