Lets assume I have $Ax=b$ equation, where $A$ is $2$x$2$ matrix.
1) I want to find an A, x, and b such that relative error in x is small but absolute error in x is large
2) Also want to find A, x, and b such that absolute error is small and relative error in x is large
I know the following formulas:
$ABS_{error}=\|\hat{x}-x\|^2$
$REL_{error}=ABS_{error}/\|x\|$
I was thinking to do reverse engineering to find $A$ and $b$ based on $x$ and $\hat{x}$, but then i did not know how should i find $\hat{x}$? Which method should I use?
Help please