engineering recuitment GATE EE 2023-24 Test Series Engineering Mathematics Linear Algebra Eigenvectors
Let A be (n x n) real valued square symmetric matrix of rank 2 with \(\mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n A_{ij}^2 = 50\). 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?1
Both I and II
2
I only
3
II only
4
Neither I nor II