Now extend this idea to a system of linear equations. (a) With Gaussian elimination, so...

Now extend this idea to a system of linear equations.

(a) With Gaussian elimination, solve the linear system

using three significant digits. Begin by pivoting on 0.400 and take each calculation to three significant digits. You should obtain the “solution” x = -1.00, y = 1.01. Check that the actual solution is x= 1.00, y = 1.00. This is a huge error—200% in the x value! Can you discover what caused it?

(b) Solve the system in part (a) again, this time interchanging the two equations (or, equivalently, the two rows of its augmented matrix) and pivoting on 75.3. Again, take each calculation to three significant digits. What is the solution this time?