Compute the following-i - a b- -b a - a b- b a -ii - a 2 - b 2 b 2 - c 2- a 2 - c 2 a 2 - b 2 - 2ab 2bc- -2ac -2ab -iii - -1 8 2 4 5 8 -6 16 5 - - 12 8 3 7 0 2 6 5 4 -iv - cos 2 x sin 2 x- sin 2 x cos 2 x - sin 2 x cos 2 x- cos 2 x sin 2 x -

(i) [ a amp; b; b amp; a ]+[ a amp; b; b amp; a ]=[ a+a amp; b+b; b+b amp; a+a ]=[ 2a amp; 2b; 0 amp; 2a ] (ii) ...

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Singular and Non Singualar Matrices

Compute the f...

Question

Compute the following:
(i) $[\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]$
(ii) $[\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$
(iii) $⎡ ⎢ ⎣ \begin{matrix} - 1 82 \end{matrix} \begin{matrix} 458 \end{matrix} \begin{matrix} - 6 165 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 1283 \end{matrix} \begin{matrix} 702 \end{matrix} \begin{matrix} 654 \end{matrix} ⎤ ⎥ ⎦$
(iv) $[\begin{matrix} {cos}^{2} x & {sin}^{2} x {sin}^{2} x & {cos}^{2} x \end{matrix}] + [\begin{matrix} {sin}^{2} x & {cos}^{2} x {cos}^{2} x & {sin}^{2} x \end{matrix}]$

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Compute the following:

(i) (ii)

(iii)

(v)

A = [\begin{matrix} cos x & sin x - sin x & cos x \end{matrix}]

A^{2} = [\begin{matrix} cos 2 x & sin 2 x - sin 2 x & cos 2 x \end{matrix}] a n d A^{^{'}} A = I

(a^{2} - b^{2}) (b^{2} + c^{2}) = (b^{2} - c^{2}) (a^{2} + b^{2})

a (b^{2} + c^{2}) = c (a^{2} + b^{2})

A = [\begin{matrix} 2 & - 1 0 & 1 \end{matrix}]

B = [\begin{matrix} 1 & 0 - 1 & - 1 \end{matrix}],

(A + B)^{2} = A^{2} + A B + B A + B^{2} = A^{2} + 2 A B + B^{2}

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