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GATE 2022 MT – Question 42

Engineering Mathematics · Linear algebra and matrices · 2 marks · Multiple choice

A $3\times3$ matrix has determinant −48 and trace 8. If one eigenvalue is 4, the other two are

  1. 2, −3
  2. 1, −3
  3. 6, −2
  4. −4, 0

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Correct answer: (C) 6, −2

Explanation

Trace gives $\lambda_2+\lambda_3=8-4=4$. Determinant gives $\lambda_2\lambda_3=-48/4=-12$. The roots of $\lambda^2-4\lambda-12=0$ are 6 and −2. Answer: **C**.