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Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are

  1. $1$ and $1$
  2. $1$ and $-1$
  3. $j$ and $-j$
  4. $pq$ and $-pq$
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answer -B (1AND-1)

SOLUTION

FORMULA OF EIGEN VALUE

A^2+(diagonal addition)A+(determinant of matrix)=0

where A  is eign value

diagonal addition (p-p)=0

det(matrix)=(-p^2-q^2)

given question (p^2+q^2)=1

then put value

A^2-1=0

the A=1and -1(ans)
by (280 points)
Answer:
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