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GATE 2026 AG – Question 37

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

A 2×2 matrix has determinant 1.6 and eigenvalue sum −2.8. Find its eigenvalues.

  1. −2 and −0.8
  2. −1.8 and −1
  3. −3 and 0.2
  4. −1.2 and −1.6

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Correct answer: (A) −2 and −0.8

Explanation

The eigenvalues have sum equal to the trace and product equal to the determinant. Their characteristic equation is $\lambda^2+2.8\lambda+1.6=0=(\lambda+2)(\lambda+0.8)$. Hence they are **−2 and −0.8, A**.

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