Gate2017 cs Q64

64Let A be real valued square symmetric matrix of rank 2 with

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?

Option : B
Explanation :
ρ(A) = n|A| = 0 ⇒ one eigen value must be ‘0’ ∈ [-5, 5]
∴ (I) is true

but eigen values of A are 0, −5,5
∴ The eigen value with the largest magnitude is not greater than 5
For and Let ⇒ eigen values = 5,5
∴ One eigen value must be in [−5,5] and largest eigen value magnitude is not greater than 5
∴ (II) is false

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