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MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES2 Marks
Question
Construct a 2 × 2 matrix, A = $[\text{a}_{\text{ ij}}]$, whose elements are given by:$\text {a}_\text {ij}=\frac {(\text{i}+2 \text{j})^{2}}{2} $
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Answer

$\text A=\left[\text {a}_{\text {ij}} \right]\text{is}\ 2\times2\ {\text {matrix where}}\ \text {a}_{\text {ij}}=\frac{(\text{i}+2 \text{j})^{2}}{2}$$\therefore\ \text{a}_{11}=\frac{(1+2)^2}{2}=\frac{9}{2}$, $\text{a}_{12}=\frac{(1+4)^2}{2}=\frac{25}{2}$
$\text{a}_{21}=\frac{(2+2)^2}{2}=\frac{16}{2}=8,$ $\text{a}_{22}=\frac{(2+4)^2}{2}=\frac{36}{2}=18 $
$\therefore\ \ \text{A}=\begin{bmatrix}\frac{9}{2}& \frac{25}{2} \\8 & 18 \end{bmatrix} $

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