Link to this document's Jupyter Notebook

In order to successfully complete this assignment, you must do the required reading, watch the provided videos, and complete all instructions. The embedded survey form must be entirely filled out and submitted on or before 11:59pm on the day before class. Students must come to class the next day prepared to discuss the material covered in this assignment.

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Pre-Class Assignment: Solve Linear Systems of Equations

Goals for today's pre-class assignment

1. Review: Methods for Solving System of Equations

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1. Review: Methods for Solving System of Equation

In this course, we talked about many different ways to solve the system of equations. In this pre-class assignment, we review some methods to solve $$Ax=b$$ with a square and full rank matrix $A$.

Consider the following system of equations:

$$\begin{bmatrix}5&-2&2 \\ 4 & -3 &4 \\ 4& -6 &7 \end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}1\\2\\3\end{bmatrix}$$

import numpy as np
import sympy as sym

A = np.matrix([[5, -2, 2], [4, -3, 4], [4,-6,7]])
b = np.matrix([[1],[2],[3]])
display(sym.Matrix(A))
display(sym.Matrix(b))

$\displaystyle \left[\begin{matrix}5 & -2 & 2\\4 & -3 & 4\\4 & -6 & 7\end{matrix}\right]$

$\displaystyle \left[\begin{matrix}1\\2\\3\end{matrix}\right]$

Iterative algorithms (Gauss-Seidel and Jacobian):

• They may require many iterations
• Gauss-Seidel is faster than Jacobian
• They do not work for all square invertible systems.

Non-iterative algorithms:

• Gauss elimination (rref)
• LU decomposition
• Find the inverse of the matrix $A$ and $x= A^{-1}b$

✅ **DO THIS:** Pick at least two methods to solve the system of equations and compare them.

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2. Assignment wrap-up

Please fill out the form that appears when you run the code below. You must completely fill this out in order to receive credit for the assignment!

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✅ **QUESTION:** How well do you feel this assignment helped you to achieve a better understanding of the above mentioned topic(s)?

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from IPython.display import HTML
HTML(
"""
<iframe 
	src="https://cmse.msu.edu/cmse314-pc-survey" 
	width="100%" 
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	frameborder="0" 
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</iframe>
"""
)

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Congratulations, we're done!

In order to successfully complete this assignment, you must do the required reading, watch the provided videos, and complete all instructions. The embedded survey form must be entirely filled out and submitted on or before 11:59pm on the day before class. Students must come to class the next day prepared to discuss the material covered in this assignment.

Course Resources:

• MTH314 Course Website

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Written by Dr. Dirk Colbry, Michigan State University
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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