Consider the 5 × 5 matrix A = \left[\begin{array}{ccccc}1 & 2 & 3 & 4 & 5 \ 5 & 1 & 2 & 3 & 4 \ 4 & 5 & 1 & 2 & 3 \ 3 & 4 & 5 & 1 & 2 \ 2 & 3 & 4 & 5 & 1 \ ]\end{array}. It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

GATE Electronics and Communications (EC) 2017 Shift 1 Solved Paper

Question : 11 of 65

Marks: +1, -0

Consider the 5 × 5 matrix

A = {[\table 1 , 2 , 3 , 4 , 5 ; 5 , 1 , 2 , 3 , 4 ; 4 , 5 , 1 , 2 , 3 ; 3 , 4 , 5 , 1 , 2 ; 2 , 3 , 4 , 5 , 1 ; ]}

.
It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

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