CSIR UGC NET June 2019 Part B Question 29

Question

Which of the following matrices is not diagonalizable over $\mathbb{R}$?

1. $\left(\begin{array}{lll}2 & 0 & 1 \\ 0 & 3 & 0 \\ 0 & 0 & 2\end{array}\right)$

2. $\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$

3. $\left(\begin{array}{lll}2 & 1 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3\end{array}\right)$

4. $\left(\begin{array}{cc}1 & -1 \\ 2 & 4\end{array}\right)$