Compute the following-a - 2- b - 2 - b - 2- c - 2 1a - 2- c - 2 - a - 2- b - 2lendbmatrix - bmatrix 2 ab - 2 bcll-2 a c -2 a blendbmatrix

[ a^2+b^2 amp; b^2+c^2; a^2+c^2 amp; a^2+b^2 ]+[ 2ab amp; 2bc; 2ac amp; 2ab ]=[ a^2+b^2+2ab amp; b^2+c^2+2ab; a^2+c^2 2ac amp; ...

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Byju's Answer

Standard XII

Mathematics

Equality of Matrices

Compute the f...

Question

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

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Solution

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

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Similar questions

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

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

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

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