Let A be n × n real valued square symmetric matrix of rank 2 with \[\sum\limits_{{\text{i}} = 1}^{\text{n}} {\sum\limits_{{\text{j}} = 1}^{\text{n}} {{\text{A}}_{{\text{ij}}}^2} } = 50.\] Consider the following statements.
I. One eigen value must be in [-5, 5]
II. The eigen value with the largest magnitude must be strictly greater than 5.
Which of the above statements about eigen values of A is/are necessarily CORRECT?
A. Both I and II
B. I only
C. II only
D. Neither I nor II
Answer: Option B
This Question Belongs to Engineering Maths >> Linear Algebra
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