Scientific Computing Using Python - PHYS:4905 - Fall 2018
Homework #7
Due 9/18/2018


Name _______________________________________________

The answers to questions 1 and 2 must be hand written on paper.  The answer to question 3 must be turned in electronically via ICON.


1. (10) Using your solution to problem #1 on homework #5 (and maybe homework #6), write down a set of matrices that will change the matrix below to the identity matrix.  Label them as E₁, E₂, .E₃, ... where E₁ is the first operation, E₂ is the second operation, etc.

$M = \left(\begin{array}{cc|l} 1 & 1 \\ 2 & -1 \\ \end{array}\right)$



2. (10) Write down an equation for the inverse of matrix M in problem #1 in terms of E₁, E₂, .E₃, ... from problem #1.  Do the matrix multiplication to find M^-1 showing the result of each matrix multiplication.  Then multiply M^-1 M to check your answer.



3. (40) Write a program to do Gaussian elimination on an augmented matrix with any number of rows.  Test your program using the three augmented matrices from homework #6.  And the examples on this page, https://en.wikipedia.org/wiki/Gaussian_elimination.