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} $

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Answer

A = $[\text a_{\text {ij}}]$ is 2 × 2 matrix where $\text a_{\text {ij}}$ = $\frac{\text {i}}{\text{j}}$$\therefore\ \text a_{\text {11}}=\frac{\text 1}{\text 1}=1 $, $\text a_{\text {12}}=\frac{\text 1}{\text 2} $
$\text a_{\text {21}}=\frac{\text 2}{\text 1}=2 $, $\text a_{22}=\frac{2}{2}=1 $
$\therefore\ \text A=\begin{bmatrix} 1& \frac{1}{2} \\2& 1 \end{bmatrix}$

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