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GATE 2022 ES – Question 37

Mathematics Foundation · Linear Algebra · 2 marks · Multiple choice

Find eigenvalues of $\begin{pmatrix}0&1\\-2&3\end{pmatrix}$.

  1. 1 and 2
  2. 1 and 3
  3. 1 and−2
  4. 0 and 3

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Correct answer: (A) 1 and 2

Explanation

The characteristic determinant is $(-\lambda)(3-\lambda)+2=\lambda^2-3\lambda+2=(\lambda-1)(\lambda-2)$. Its roots are **1 and 2,A**. Their sum3 and product2 also match trace and determinant.

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