Question

The number of distinct eigen values of the matrix

A = $\left[\begin{array}{cccc}2& 2& 3& 3\\ 0& 1& 1& 1\\ 0& 0& 3& 3\\ 0& 0& 0& 2\end{array}\right]$ is equal to

Answer 1

A = $\left[\begin{array}{cccc}2& 2& 3& 3\\ 0& 1& 1& 1\\ 0& 0& 3& 3\\ 0& 0& 0& 2\end{array}\right]$

Given 'A' matrix is a upper triangular matrix so, diagonal elements are its eigen values

${\lambda }_1=2,{\lambda }_2=1,{\lambda }_3=3,{\lambda }_4=2$

So, there are three distinct eigen values of the matrix.