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  • Compute the following: (iv) [cos^2x sin^2x; sin^2x cos^2x] + [ sin^2x cos^2x; cos^2x sin^2x]

Q2.    Compute the following:

            (iv) \begin{bmatrix} \cos^2 x &\sin^2 x\\ \sin^2 x & \cos^2x \end{bmatrix} + \begin{bmatrix} \sin^2 x &\cos^2 x\\ \cos^2 x & \sin^2x \end{bmatrix}

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best_answer

    (iv) the addition is done as follows

 \begin{bmatrix} \cos^2 x &\sin^2 x\\ \sin^2 x & \cos^2x \end{bmatrix} + \begin{bmatrix} \sin^2 x &\cos^2 x\\ \cos^2 x & \sin^2x \end{bmatrix}

        =\begin{bmatrix} \cos^2+ \sin^2 x &\sin^2 x+\cos^2 x\\ \sin^2 x+\cos^2 x & \cos^2x+ \sin^2 x \end{bmatrix}      since  sin^2x+cos^2x=1

         =\begin{bmatrix} 1 &1\\ 1 & 1 \end{bmatrix}  

Posted by

seema garhwal

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