Compute the following: (i)[ab−ba]+[abba] (ii)[a2+b2b2+c2a2+c2a2+b2]+

1.	Compute the following: (i)[ab−ba]+[abba] (ii)[a2+b2b2+c2a2+c2a2+b2]+[2ab2bc−2ac−2ab] (iii)⎡⎢⎣−14−68516285⎤⎥⎦+⎡⎢⎣1276805324⎤⎥⎦ (iv)[cos2xsin2xsin2xcos2x]+[sin2xcos2xcos2xsin2x]
Answer» Compute the following: $(i) [\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]$ $(i i) [\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$ $(i i i) ⎡ ⎢ ⎣ \begin{matrix} - 1 & 4 & - 6 8 & 5 & 16 2 & 8 & 5 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 12 & 7 & 6 8 & 0 & 5 3 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦$ $(i v) [\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}]$

Compute the following: (i)[ab−ba]+[abba] (ii)[a2+b2b2+c2a2+c2a2+b2]+[2ab2bc−2ac−2ab] (iii)⎡⎢⎣−14−68516285⎤⎥⎦+⎡⎢⎣1276805324⎤⎥⎦ (iv)[cos2xsin2xsin2xcos2x]+[sin2xcos2xcos2xsin2x]

Answer»

Compute the following:
$(i) [\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]$

$(i i) [\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$

$(i i i) ⎡ ⎢ ⎣ \begin{matrix} - 1 & 4 & - 6 8 & 5 & 16 2 & 8 & 5 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 12 & 7 & 6 8 & 0 & 5 3 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦$

$(i v) [\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}]$

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