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GATE 2026 BM – Question 15

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Find the eigenvalues of $P=\begin{pmatrix}1&-2\\3&-4\end{pmatrix}$.

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

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Correct answer: (A) −1 and −2

Explanation

The trace is −3 and determinant is −4+6=2. Thus the characteristic polynomial is $\lambda^2+3\lambda+2=(\lambda+1)(\lambda+2)$. Its roots are −1 and −2, A.

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