Question

Consider the matrix:

P = $\left[\begin{array}{ccc}1& 1& 0\\ 0& 1& 1\\ 0& 0& 1\end{array}\right]$

The number of distinct eigenvalues of P is:

• A. 3
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is C 1

$|P-\lambda I|$ = $\left|\begin{array}{ccc}1-\lambda & 1& 0\\ 0& 1-\lambda & 1\\ 0& 0& 1-\lambda \end{array}\right|$

$(1-\lambda )\left[\right(1-\lambda \left)\right(1-\lambda )-0]$ = 0

$\lambda$ = 1, 1, 1

No. of distinct eigen value = 1.