Question
Let p and q be real numbers such that p2 + q2 = 1. The eigenvalues of the matrix are
Options :
1 and 1
1 and -1
j and −j
pq and −pq
Answer :
1 and -1
Solution :
Let the Eigenvalues be a, b
Determinant of matrix = -p2 - q2 = - 1
Product of Eigenvalues = a × b = -1 Checking from the given option ⇒ a = 1, b = - 1.
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