GATE Electrical Engineering (EE) 2021 Solved Papers

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Question : 22 of 65

Marks: +1, -0

Let

p

and

q

be real numbers such that

p^{2}+q^{2}=1

. The eigenvalues of the matrix

[\table p , q ; q , -p]

are:

${j}$ and $- {j}$
pq and -pq
1 and 1
1 and $-1$

Solution:

Let A=[\table p , q ; q , -p]

The characteristic equation

| {A}-λ {I}|=0

|\table p-λ , q ; q , -p-λ|=0

⇒( {p}^{2}-λ^{2})- {q}^{2}=0

⇒ 1-λ^{2}=0

λ^{2}=1

λ=± 1

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