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Engineering Maths · Q20

Linear Algebra

Engineering and GATE · Engineering Maths · question 20

Q20

Consider the 5 × 5 matrix \[ A = [ array*20c 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 array ]\] It is given that A has only one real eigen value. Then the real eigen value of A is

Consider the 5 × 5 matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}} 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}} \right]
It is given that A has only one real eigen value.
Then the real eigen value of A is
A.
-2.5
B.
0
C.
15
Answer
D.
25

Answer: Option C

Solution

Answer: Option C
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