Construct a 2 × 2 matrix, A = [ a_ ij ], whose elements are given… - Vidyadip

Question

Construct a 2 × 2 matrix, A = $[\text a_{\text {ij}}]$, whose elements are given by:$\text a_{\text{ij}}=\frac{(\text{i}+\text{j})^2} {2} $

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Answer

A = $[\text a_{\text{ ij}}]$ is 2 × 2 matrix where, $\text a_{\text{ij}}=\frac{(\text{i}+\text{j})^2} {2} $$\therefore\ \ \text{a}_{11}=\frac{(1+1)^2}2=\frac{4}{2}=2$, $\text a_{12}=\frac{(1+2)^2}{2}=\frac{9}{2} $
$\text a_{21}=\frac{(2+1)^{2}}{2}=\frac{9}{2} $, $\text a_{23}=\frac{(2+2)^{2}}{2}=\frac{16}{2}=8 $
$\therefore\ \text A= \begin{bmatrix}2 & \frac{9}{2} \\ \frac{9}{2} & 8 \end{bmatrix} $

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