The GATE Grind

GATE 2019 ME (ME2) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

In $[A]\{X\}=\{R\}$, $$A=\begin{bmatrix}4&8&4\\8&16&-4\\4&-4&15\end{bmatrix},\quad X=\begin{bmatrix}2\\1\\4\end{bmatrix},\quad R=\begin{bmatrix}32\\16\\64\end{bmatrix}.$$ Which is an eigenvalue of A?

  1. 4
  2. 8
  3. 15
  4. 16

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) 16

Explanation

The given vectors satisfy $R=16X$. Thus $AX=16X$ for nonzero X, exactly the eigenvector equation. Therefore **16, D**, is an eigenvalue.