Question

(b) Show by example that the solution of$\mathit{a}\mathit{x}\mathbf{=}\mathit{b}$ may not be the same as the solution of $\mathit{y}\mathit{a}\mathbf{=}\mathit{b}$. [Hint: Consider ${\mathit{S}}_3$.]

Short answer

Consider the example $\left(\mathrm{12}\right)x=\left(\mathrm{23}\right)$and $y\left(\mathrm{12}\right)=\left(\mathrm{23}\right)$, we have shown that the solution of$ax=b$ may not be the same as the solution of $ya=b$.

Step-by-step solution

Determine given function

Consider the given functions,$ax=b$ and $ya=b$.

Determine the examples

Here$S_3$ is the solution for,

$\left(\mathrm{12}\right)x=\left(\mathrm{23}\right)$

Where, $x=\left(\mathrm{123}\right)$.

Solution for$y\left(\mathrm{12}\right)=\left(\mathrm{23}\right)$ and $y=\left(\mathrm{132}\right)$.

Consider the example$\left(\mathrm{12}\right)x=\left(\mathrm{23}\right)$ and $y\left(\mathrm{12}\right)=\left(\mathrm{23}\right)$, we have shown that the solution of$ax=b$ may not be the same as the solution of$ya=b$.