If-A - - cos - amp- sin - sin - amp- - cos - - B - - 1 amp- 0- -1 amp- 1 - C - ABA-T- then-A-TC-nA-equals-to -n - Z- -n amp- 1- 1 amp- 0 - 1 amp- -n- 0 amp- 1 - 0 amp- 1- 1 amp- -n - 1 amp- 0- -n amp- 1 -

The correct option is D [ 1 amp; 0; n amp; 1 ]A = [ cosθ amp; sinθ; sin θ amp; cos θ ] AA^T = I (i) Now, C = ABA^T ⇒ A^TC ...

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Transpose Conjugate

If A = [ ...

Question

$I f A = [\begin{matrix} c o s θ & s i n θ s i n θ & - c o s θ \end{matrix}], B = [\begin{matrix} 1 & 0 - 1 & 1 \end{matrix}], C = A B A^{T}, t h e n A^{T} C^{n} A e q u a l s t o (n ϵ Z^{+})$

[\begin{matrix} - n & 1 1 & 0 \end{matrix}]

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[\begin{matrix} 1 & - n 0 & 1 \end{matrix}]

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[\begin{matrix} 0 & 1 1 & - n \end{matrix}]

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[\begin{matrix} 1 & 0 - n & 1 \end{matrix}]

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I f A = [\begin{matrix} c o s θ & s i n θ s i n θ & - c o s θ \end{matrix}], B = [\begin{matrix} 1 & 0 - 1 & 1 \end{matrix}], C = A B A^{T}, t h e n A^{T} C^{n} A e q u a l s t o (n ϵ Z^{+})

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