Gate 2016 EE (Set 1) Q2

2. Consider a $$ 3\times 3 $$ matrix with every element being equal to 1. Its only non-zero eigenvalue is:—–
Solution:
Consider $$ A_{3\times3}$$=$$\begin{bmatrix} 1& 1 &1 \\ 1& 1 &1 \\ 1& 1 &1 \end{bmatrix}$$
Order of the matrix=3
Let eigen value $$ \lambda$$
Then $$ \lambda$$=1 $$\times$$ order of the matrix (i.e. 3)
=$$1\times 3 =3$$
$$\therefore$$ Answer: 3

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