Introduction
In this Section we will reconsider the Gaussian elimination approach discussed in HELM booklet 8, and we will see how rounding error can grow if we are not careful in our implementation of the approach. A method called partial pivoting, which helps stop rounding error from growing, will be introduced.
Prerequisites
 revise matrices, especially matrix solution of equations
 recall Gaussian elimination
 be able to find the inverse of a $2\times 2$ matrix
Learning Outcomes

carry out Gaussian elimination with
partial pivoting