Scientific Computing Using Python - PHYS:4905 - Fall 2018
Homework #9
Due 10/2/2018


Name _______________________________________________

The answers to these questions must be hand written and handed in on paper.


1. (25) Find the inverse of the matrix $\begin{pmatrix} a & b & c \\ 0 & d & e \\ 0 & 0 & f \end{pmatrix}$.

When is this matrix singular?


2. (18) Let $M = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ and $N = \begin{pmatrix} x & y \\ z & w \end{pmatrix}$. Compute the following:

(a) det(M)
(b) det(N)
(c) MN
(d) det(MN)
(e) The product of your answers to (a) and (b).
(f) How do (d) and (e) compare?


3. (15) Using Cramer's rule, find the inverse of $\begin{pmatrix} 2 & 0 & 1 \\ 7 & 0 & 2 \\ 6 & 2 & 6 \end{pmatrix}$.  Write out the adjoint matrix before evaluating the determinants and then again after.  Check your answer.