Compute the following: left[ {begin{array}{cc | vedclass

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(A) To compute the sum of the two matrices,we add the corresponding elements of each matrix: $\left[\begin{array}{cc}\cos ^{2} x & \sin ^{2} x \ \sin

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$\left[\begin{array}{cc}1 & 1 \ 1 & 1\end{array}ight]$

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(A) To compute the sum of the two matrices,we add the corresponding elements of each matrix: $\left[\begin{array}{cc}\cos ^{2} x & \sin ^{2} x \ \sin ^{2} x & \cos ^{2} x\end{array}ight]+\left[\begin{array}{cc}\sin ^{2} x & \cos ^{2} x \ \cos ^{2} x & \sin ^{2} x\end{array}ight]$$= \left[\begin{array}{cc}\cos ^{2} x+\sin ^{2} x & \sin ^{2} x+\cos ^{2} x \ \sin ^{2} x+\cos ^{2} x & \cos ^{2} x+\sin ^{2} x\end{array}ight]$Using the trigonometric identity $\sin^2 x + \cos^2 x = 1$,we substitute the value into the matrix:$= \left[\begin{array}{cc}1 & 1 \ 1 & 1\end{array}ight]$

Compute the following: $\left[ {\begin{array}{cc} {{\cos }^2}x & {{\sin }^2}x \\ {{\sin }^2}x & {{\cos }^2}x \end{array}} \right] + \left[ {\begin{array}{cc} {{\sin }^2}x & {{\cos }^2}x \\ {{\cos }^2}x & {{\sin }^2}x \end{array}} \right]$

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