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GATE 2019 MT – Question 11

Engineering Mathematics · Linear algebra and matrices · 1 mark · Multiple choice

One eigenvalue of $\begin{pmatrix}a&2\\8&a\end{pmatrix}$ is

  1. $a-4$
  2. $-a-4$
  3. 4
  4. −4

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Correct answer: (A) $a-4$

Explanation

The characteristic equation is $(a-\lambda)^2-16=0$. Thus the eigenvalues are a+4 and a−4. The latter appears as A. The off-diagonal product, rather than their sum, determines the squared separation from a.

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