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.


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.


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:

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.

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