Problem
Implement Gaussian elimination for solving systems of equations, C ·X = Y. Compare your implementation against a popular library routine for:
(a) Speed: How does the run time compare, for both dense and sparse coefficient matrices?
(b) Accuracy: What are the size of the numerical residuals CX - Y, particularly as the condition number of the matrix increases.
(c) Stability: Does your program crash on a singular matrix? What about almost singular matrices, created by adding a little random noise to a singular matrix?