GATE2019 ME-1: 1

Question

Consider the matrix

$$P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$

The number of distinct eigenvalues

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

There will be 3 Eigen values which are 1,1,1. All of these are same so the no of distinct Eigen values will be 1.

Right answer will be option  (B) 1

Comments

Question asks 'The number of distinct eigenvalues'? 1,1,1 so no one is distinct. Answer should be 0 but all answers over internet and book says 1 which is confusing to me. 1 is similar to 1 and another 1. So no distinct eigenvalues. Thus 0.