Let A = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − 1 0 2 2 1 and P = , cos sin sin cos ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ θ θ − θ θ 0. If B = PAP T , C = P T B 10 P and the sum of the diagonal elements of C is n m , where gcd(m, n) = 1, then m + n is:

Question

Let A = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − 1 0 2 2 1 and P = , cos sin sin cos ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ θ θ − θ θ > 0. If B = PAP T , C = P T B 10 P and the sum of the diagonal elements of C is n m , where gcd(m, n) = 1, then m + n is:

Accepted Answer

65

Let A = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − 1 0 2 2 1 and P = , cos sin sin cos ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ θ θ − θ θ > 0. If B = PAP T , C = P T B 10 P and the sum of the diagonal elements of C is n m , where gcd(m, n) = 1, then m + n is:

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