Floating point problem from Quiz 1

audrey

Here's the third problem from Quiz 1 on Gaussian elimination with floating point arithmetic:

Consider the system
$$
\left(\begin{matrix}
0.01 & 1 \\ 1000 & 2
\end{matrix}\right)
\left(\begin{matrix}x\\ y \end{matrix}\right) =
\left(\begin{matrix}1.01\\ 1002 \end{matrix}\right).
$$
Note that $x=y=1$ is an exact solution.

1. Solve the system using Gaussian elimination with three-digit rounding.
2. Solve the system using Gaussian elimination with partial pivoting and three-digit rounding.

I found that both methods 1 and 2 yielded the exact solution. What's up with that?