Compute [ ll a^ 2 +b^ 2 & b^ 2 +c^ 2 a^ 2 +c^ 2 & a^ 2 +b^ 2 ]+ [… - Vidyadip

Question

Compute $\left[\begin{array}{ll} {a^{2}+b^{2}} & {b^{2}+c^{2}} \\ {a^{2}+c^{2}} & {a^{2}+b^{2}} \end{array}\right]+\left[\begin{array}{cc} {2 a b} & {2 b c} \\ {-2 a c} & {-2 a b} \end{array}\right]$

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Answer

$\left[\begin{array}{ll} {a^{2}+b^{2}} & {b^{2}+c^{2}} \\ {a^{2}+c^{2}} & {a^{2}+b^{2}} \end{array}\right]+\left[\begin{array}{cc} {2 a b} & {2 b c} \\ {-2 a c} & {-2 a b} \end{array}\right]$
$=\left[\begin{array}{ll} {a^{2}+b^{2}+2 a b} & {b^{2}+c^{2}+2 b c} \\ {a^{2}+c^{2}-2 a c} & {a^{2}+b^{2}-2 a b} \end{array}\right]$
$=\left[\begin{array}{ll} {(a+b)^{2}} & {(b+c)^{2}} \\ {(a-c)^{2}} & {(a-b)^{2}} \end{array}\right]$

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