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GATE 2020 PI – Question 37

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

Which pair consists of eigenvectors of $A=\begin{pmatrix}1&5\\3&3\end{pmatrix}$?

  1. (1,−1) and (3,−3)
  2. (1,1) and (−5/3,1)
  3. (1,3) and (5,3)
  4. (−1,1) and (5/3,1)

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Correct answer: (B) (1,1) and (−5/3,1)

Explanation

Multiply A by(1,1): the result(6,6)=6(1,1). Multiplying by(−5/3,1) gives(10/3,−2)=−2(−5/3,1). Both are eigenvectors with distinct eigenvalues6 and−2. Therefore B.

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