Programming Deliverables$/$TASKS:

$1.$ Download PETE$301\_$Lab$5.$zip and unzip all the files into a folder

$2.$ Develop codes for the Na$$ve Gaussian Elimination $($GE$)$ as described in class. You can use the

idea of three for loops to eliminate elements in the columns $($that is$,$ zero out elements below

the diagonal $).$

$3.$ Once you coded your na$$ve GE$,$ reshape the code to function more efficiently using the

vectorization approach.

$4.$ Study and understand the GE with Pivoting My$\_$GE$\_$naive$\_$pivot.py

$5.$ Implement the GE of $(2)$ and $(3)$ and compare with the bulti$-$in functions in Python

a$.$ Use the built$-$in solver np$.$linalg.solve$($A$,$ B$)$ to solve the linear system

b$.$ Use the built$-$in function to compute the LU decomposition of a matrix.

P$,$ L$,$ U $=$ scipy.linalg.lu$($A$).$