(i) One eigenvalue must be in [-5, 5]. (ii) The eigenvalue with the largest magnitude must be strictly greater than 5.
Which of the above statements about engenvalues of A is/are necessarily CORRECT?
(A) Both (i) and (ii)
(B) (i) only
(C) (ii) only
(D) Neither (i) nor (ii)
Explanation: As a rank of A matrix = 2, hence
=> n-2 eigen values are zero. Let be the eigen values.
Given that ————(1)
We know that Trace of (AA)T = Trace of A2 (since A is symetric) = ————(2)
From (1) and (2) :
Hence, atleast one of the given eigen values lies in [-5,5](only 1 is correct).
This solution is contributed by Sumouli Chaudhary.
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