# Math 150: Linear Algebra

## Final Exam Review

### Course Information

Instructor: Dr. Lauren Williams
Class Meeting: MWF 9:15 - 10:20 Hirt 209; T 9:50 - 11:30 Old Main Advanced Lab
My Office: Old Main 404 (Tower)
My Office Hours: Mon 2:15 - 3:30, Tues 11:45 - 1, Wed 2:15 - 3:30, Thur 11:30 - 2

### Course Description

This is a one semester course in linear algebra with computer applications. We will be covering the following topics: matrices and matrix properties, vectors and vector spaces, linear systems, and linear transformations. The class lectures will focus primarily on definitions and theory, with some simple calculations being performed without the aid of a computer. After learning the basic principles and theory of each topic, we will reinforce the material using the open source mathematics software SAGE. Through a series of lab experiments, you will also gain familiarity with the programming language Python. Many of these lab experiments will focus on applications of linear algebra to other areas of mathematics and other fields, including data science.

Topics will include vectors and vector arithmetic, solutions of linear systems, LU factorization, vector spaces and subspaces, the four fundamental subspaces, projections, determinants, eigenvalues and eigenvectors, symmetry, singular value decomposition, linear transformations, and applications.

### Course Objectives

On successful completion of the course, students should be able to:
• describe the solution(s) of a system of linear equations, or be able to decide that one does not exist.
• be able to perform arithmetic operations on vectors and matrices, where defined.
• calculate the determinant of a matrix, and understand its significance.
• define a vector space and determine whether a set is a vector space.
• find the basis and dimension of a vector space.
• define and describe the four fundamental subspaces.
• define and identify linear maps.
• define and compute eigenvalues and eigenvectors.
• explain the geometric effect of a linear transformation on 2-dimensional spaces.
• produce and utilize simple Sage programs to perform computations related to all of the above topics.

### Textbook and Materials

Introduction to Linear Algebra, by Gilbert Strang, 4th Edition (older editions are fine too). No other supplies are required for the course.

### Homework

You will be given take home assignments, usually every week. These assignments will include questions taken directly from the text as well as additional problems related to topics we’ll see in class. Late work will not be accepted. The assignments will be posted on the course website (not Blackboard), along with solutions after assignments are due. Your lowest homework grade will be dropped when calculating your final grade.

### Lab Assignments

In addition to the homework assignments, you will have a weekly lab assignment. These will typically be completed during the lab meetings. If you need additional time on the lab, or if you are absent, the lab work may be completed at home and turned in by Friday of the week the assignment is given. Your lowest lab assignment grade will be dropped when calculating your final grade.

Lab assignments will be completed online through Sage Cloud. You do not need to purchase any software or equipment for the labs, and you are free to use your own computer if you prefer. To work at home, you'll only need an internet connection - no software needs to be installed.

### Exams

We will have two midterm exams. You will be given an exact list of topics, along with a review sheet, approximately one week before each exam. Use of notes, textbooks, calculators, electronic devices, or other materials will not be permitted during an exam.
1. Midterm 1: Wednesday, March 9
2. Midterm 2: Wednesday, April 27
The final exam will be cumulative, and is scheduled for Friday, May 20, 8:00 - 10:00.

Your final grade will be calculated as follows:
• Average of midterm exams: 30%
• Average of homework assignments: 30%
• Average of lab assignments: 15%
• Final Exam: 25%
Quiz and exam grades will be posted on Blackboard, so you can keep track of your progress at any time.

Your letter grade will be determined according to the department grading scale:
 F D D+ C C+ B B+ A 0-59 60-64 65-69 70-77 78-83 84-89 90-93 94-100

### Course Schedule

This schedule will be kept up to date as assignments are given, or if we get behind schedule. Exam dates will not be changed as long as the University is open on those days.

 Date Topic Noteworthy Events Week 1 Feb 3 Class Introduction Feb 5 Vectors and Linear Combinations Week 2 Feb 8 Lengths and Dot Products Feb 10 Matrices Feb 12 Vectors and Linear Equations Week 3 Feb 15 Elimination Feb 17 Elimination Feb 19 Rules for Matrix Operations Week 4 Feb 22 Inverse Matrices Feb 24 Inverse Matrices Feb 26 Transposes & Permutations Week 5 Feb 29 Spaces of Vectors Mar 2 Solutions of $$Ax=0$$ Mar 4 Rank & Reduced Echelon Form Week 6 Mar 7 Review Mar 9 Midterm I Mar 11 Solutions of $$Ax=b$$ Week 7 Mar 14 Solutions of $$Ax=b$$ Mar 16 Solutions of $$Ax=b$$ Mar 18 Independence, Basis, Dimension Week 8 Mar 21-25 Easter Break Week 9 Mar 28 Easter Break Mar 30 Independence, Basis, Dimension Apr 1 Orthogonality & Projections MAA Section Meeting (April 1-2, Gannon U) Week 10 Apr 4 Determinants Apr 6 Determinants Apr 8 Cramer's Rule Week 11 Apr 11 Eigenvalues & Eigenvectors Apr 13 Eigenvalues & Eigenvectors Apr 15 Diagonalization Week 12 Apr 18 Diagonalization Apr 20 Similar Matrices Apr 22 Break Week 13 Apr 25 Review Apr 27 Midterm II Apr 29 SVD Week 14 May 2 Markov Matrices May 4 Linear Transformations May 6 Linear Transformations Week 15 May 9 Linear Transformations May 11 Linear Transformations May 13 Review Week 16 May 16 Reading Day May 18 May 20 Final Exam 8:00 - 10:00

### Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

### Support of the Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.