Setup: Each program will take a single input, the size of the Matrix, N. Your program will allocate and populate the matrix using random numbers. Your program will then start the clock. Run Gaussian Elimination and back subsitution. And then take the stop time. Your program will output the time.

Task: Create Gaussian elimination with back substitution.

Input: Size of square matrix. Size should be 250, 500, 1000, 1500, 2000

Internals: Explicitly or implicitly allocate sufficient memory to a Nx(N+1) floating point Matrix, (or NxN) + N matrices for NUMPY using a random number generator -- populate the Matrix. Perform Gaussian elimination and back subsitution on the Matrix Your routine should have no output other than the runtime

Write in :

Python+ Numpy/pivoting as LU decomposition

Python w/o Numpy

Fortran

Output:

You MUST run each experiment 5 times for each size. This means , you should have 5 runs x 5 sizes x 3 implementations =75 data points.

A table of all or your runs with the average runtime for each AND the standard deviation.

A graph plotting the three average sequences.

A SHORT paragraph comparing the three plots along with your conclusions about the data.