Let $A$ be $n \times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^n \sum_{j=1}^n A_{ij}^2 = 50$. 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?

Let A be n n real valued square symmetric matrix of rank 2 with i=1n j=1n Aij2 = 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?

Topic-wise GATE CS PYQs with verified steps