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# Compute the following : $\begin{bmatrix} cos^2x & sin^2x \\ sin^2x & cos^2x \end{bmatrix} + \begin{bmatrix} sin^2x & cos^2x \\ cos^2x & sin^2x \end{bmatrix}$

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## 1 Answer

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Toolbox:
• We know that $sin^2x+cos^2x=1$
• The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.
$\begin{bmatrix} cos^2x & sin^2x \\ sin^2x & cos^2x \end{bmatrix} + \begin{bmatrix} sin^2x & cos^2x \\ cos^2x & sin^2x \end{bmatrix} =\begin{bmatrix}cos^2x+sin^2x &sin^2x+cos^2x\\sin^2x+cos^2x&cos^2x+sin^2x\end{bmatrix}$
$\Rightarrow \begin{bmatrix}1 & 1\\1 & 1\end{bmatrix}$
answered Apr 6, 2013

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