Scientific Computing Using Python - PHYS:4905 - Fall 2018
Homework #5
Due 9/11/2018


Name _______________________________________________

The answers to this homework must be hand written on paper.  No electronic answers will be accepted.

1. (5) Apply the Gaussian elimination algorithm discussed in class to the augmented matrix below.  Write down your steps as you go.  What do you find as the solution?

$\left(\begin{array}{cc|l} 1 & 1 & | \, 27 \\ 2 & -1 & | \, 0 \\ \end{array}\right)$



2. (10) Find the augmented matrix for the system of linear equations below.  Then apply the Gaussian elimination algorithm discussed in class and write down your steps as you go.  What do you find as the solution?

$\begin{pmatrix} 1 & 2 & 3 \\ 3 & 4 & 7 \\ 6 & 5 & 9 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \\ 11 \\ \end{pmatrix}$



3. (5) Let M and N be matrices and v be a vector as defined below.

$$M = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \;\;\;\;\;\; N = \begin{pmatrix} e & f \\ g & h \end{pmatrix} \;\;\;\;\;\; u = \begin{pmatrix} x \\ y \end{pmatrix} \;\;\;\;\;\; v = \begin{pmatrix} x \\ y \end{pmatrix}$$
Write down the set of equations corresponding to Nv = u and MNv = u.  Are these equations linear in x and y?