Scientific Computing Using Python - PHYS:4905
Homework #7
Due 9/19/2019


Name _______________________________________________

This homework must be hand written on paper with work shown.


1. (5) Show that the inverse of the product is the product of the inverses with the order swapped, (AB)-1=B-1A-1(AB)^{-1} = B^{-1} A^{-1}.


2. (10) 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=(112-1)M = \left(\begin{array}{cc|l} 1 & 1 \\ 2 & -1 \\ \end{array}\right)


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