The GATE Grind

GATE 2022 CS – Question 53

Engineering Mathematics · Linear Algebra · 2 marks · Multiple select

Which of the following is/are the eigenvector(s) for the matrix given below?
$\begin{pmatrix}-9&-6&-2&-4\\-8&-6&-3&-1\\20&15&8&5\\32&21&7&12\end{pmatrix}$

  1. $(-1,1,0,1)^T$
  2. $(1,0,-1,0)^T$
  3. $(-1,0,2,2)^T$
  4. $(0,1,-3,0)^T$

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Correct answer: (A) $(-1,1,0,1)^T$; (C) $(-1,0,2,2)^T$; (D) $(0,1,-3,0)^T$

Explanation

Computing $Mv$ gives: A→(−1,1,0,1)=1·v; C→(−3,0,6,6)=3·v; D→(0,3,−9,0)=3·v. B gives (−7,−5,12,25), which is not a multiple of v.