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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
Question
Compute the following:
$\begin{bmatrix}\text{a}^2+\text{b}^2 & \text{b}^2+\text{c}^2 \\ \text{a}^2+\text{c}^2 & \text{a}^2+\text{b}^2 \end{bmatrix}+\begin{bmatrix}2\text{ab} & 2\text{bc} \\-2\text{ac} &-2\text{ab}\end{bmatrix}$
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Answer

$\begin{bmatrix}\text{a}^2+\text{b}^2 &\text{b}^2+\text{c}^2\\ \text{a}^2+\text{c}^2&\text{a}^{2}+\text{b}^2\end{bmatrix}+\begin{bmatrix}\text{2ab } &\text{2bc}\\ \text{-2ac}&\text{-2ab}\end{bmatrix}$
$=\begin{bmatrix}\text{a}^2+\text{b}^2+2\text{ab} &\text{b}^2+\text{c}^2+2\text{bc}\\ \text{a}^2+\text{c}^2-2\text{ac}&\text{a}^{2}+\text{b}^2-\text{2ab}\end{bmatrix}$
$=\begin{bmatrix}(\text{a + b})^2 &(\text{b + c})^2\\ (\text{a - c})^2&(\text{a - b})^2\end{bmatrix}$

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