GATE | CS | 2017 | Set 1 | Engineering Mathematics | Linear Algebra | Question 45

Let A be m×n real valued square symmetric matrix of rank 2 with expression given below.

[Tex]\sum_{i=1}^{n} \sum_{j=1}^{n} A_{ij}^2 = 50[/Tex]

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?