Consider solving the linear system $Ax=b$ using $4-$digit decimal floating point arithmetic, where

$A=([{10}^{-4},1],[1,1]),b=(\frac{1}{2}),x$~~$(\frac{1}{1})$

Recall this question appeared on Worksheet #$3.$ Compute the weighted residual $$ and upper

bound for the relative error of the approximation in the following two cases.

$($a$)(5$ points$)$ Without a row swap. Explain your observations.

$($b$)(5$ points$)$ With a row swap. Explain your observations.