GATE | GATE-CS-2017 (Set 1) | Question 45
Let A be m×n real valued square symmetric matrix of rank 2 with expression given below.
Consider the following statements
(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 eigenvalues of A is/are necessarily CORRECT?
Both (i) and (ii)
Neither (i) nor (ii)
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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