GATE Chemical 2012 | Question: 5

Question

Consider the following $(2\times2)$ matrix

                                                                 $\left( \begin{array}{c} 4 & 0 \\ 0 & 4 \end{array} \right)$

Which one of the following vectors is $\text{NOT}$ a valid eigenvector of the above matrix ?

• A. $\left( \begin{array}{c} 1 \\ 0 \end{array} \right)$
• B. $\left( \begin{array}{c} -2 \\1 \end{array} \right)$
• C. $\left( \begin{array}{c} 4 \\ -3 \end{array} \right)$
• D. $\left( \begin{array}{c} 0 \\ 0 \end{array} \right)$

Answer 1

By definition, eigen vector can not be Zero vector

So the option D