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GATE 2026 BT – Question 12

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

Which of the following is one of the eigenvalues for the matrix given below?

$\begin{bmatrix} 3 & 4 \\ 4 & -3 \end{bmatrix}$

  1. 1
  2. 3
  3. 5
  4. 7

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Correct answer: (C) 5

Explanation

The characteristic equation is $(3 - \lambda)(-3 - \lambda) - 16 = \lambda^2 - 9 - 16 = 0$, so $\lambda^2 = 25$ and $\lambda = \pm 5$.