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GATE 2025 CE (CE2) – Question 45

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Multiple select

Pick the CORRECT eigen value(s) of the matrix [A] from the following choices.
$[A] = \begin{bmatrix} 6 & 8 \\ 4 & 2 \end{bmatrix}$

  1. 10
  2. 4
  3. -2
  4. -10

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Correct answer: (A) 10; (C) -2

Explanation

The trace is 8 and the determinant is $12 - 32 = -20$. The characteristic equation is $\lambda^2 - 8\lambda - 20 = 0$, that is $(\lambda - 10)(\lambda + 2) = 0$, so the eigenvalues are 10 and −2.