Let x = [4.0091, 0.12319, 1.2341]$^T$ and y = [-1.1021, .35449, 3.5449]$^T$. Using 3 decimal-digit arithmetic compute $\bar{x} = fl(x)$, $\bar{y} = fl(y)$, c = fl($x^T \bar{x}$) and d = fl($x^T \bar{y}$).
Now compute the actual values of $x^T x$ and $x^T y$ (to 5 or 6 significant digits) and find the relative errors
and
$\frac{|x^T x - c|}{|x^T x|}
$\frac{|x^T y - d|}{|x^T y|}.$
Note: s = fl($u^T v$) for u, v ? $R^n$ is to be computed in the standard way (the same way as the textbook problem in this homework assignment):
s=0; for j=1:n, s = fl(s + fl($u_j * v_j$)); end
