Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems If and , where , , and are real numbers, and C=(A^ -5 +B^ -5 )+5A^ -1 B^ -1 (A^ -3…
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Problem If A − 1 = [ sin 2 α 0 0 0 sin 2 β 0 0 0 sin 2 γ ] A^{-1}=\begin{bmatrix}\sin^2\alpha&0&0\\0&\sin^2\beta&0\\0&0&\sin^2\gamma\end{bmatrix} A − 1 = sin 2 α 0 0 0 sin 2 β 0 0 0 sin 2 γ B − 1 = [ cos 2 α 0 0 0 cos 2 β 0 0 0 cos 2 γ ] B^{-1}=\begin{bmatrix}\cos^2\alpha&0&0\\0&\cos^2\beta&0\\0&0&\cos^2\gamma\end{bmatrix} B − 1 = cos 2 α 0 0 0 cos 2 β 0 0 0 cos 2 γ α \alpha α β \beta β γ \gamma γ C = ( A − 5 + B − 5 ) + 5 A − 1 B − 1 ( A − 3 + B − 3 ) + 10 A − 2 B − 2 ( A − 1 + B − 1 ) , C=(A^{-5}+B^{-5})+5A^{-1}B^{-1}(A^{-3}+B^{-3})+10A^{-2}B^{-2}(A^{-1}+B^{-1}), C = ( A − 5 + B − 5 ) + 5 A − 1 B − 1 ( A − 3 + B − 3 ) + 10 A − 2 B − 2 ( A − 1 + B − 1 ) , ∣ C ∣ |C| ∣ C ∣ Browse the problem library