Math 22: Linear Algebra with Applications

Spring 2020

General Information


  • The latest homework will always appear on top.

  • If you are interested in learning to typeset mathematics here is a list of resources compiled by Rebecca Weber on LaTex

    Homework assignments

  • Late Homework will not be accepted.
  • Make sure that in your homework you indicate everyone that helped you in the homework or anyone with whom you collaborated.

    WebWork problems: These problems are very important. We will discuss most of them in class. Please be sure that you understand these problems thoroughly as you might be asked to present some of these problems in class.

    Written assignments: These problems will graded in detail and are due once a week on Wednesdays. You should make sure that they are well-written.

    Discussion assignments: There will be discussion threads in Canvas and as part of the participation grade. If students are attending our regular meetings they only have to post at least once a week. However, if you are in a time zone that doesn't allow you to participate in our regular class meetings. You have to post at least every day that we have regular meetings. There will be prompts from your professor as well as questions from other students.

    Week 10
    Friday, June 5:
    • Topic: Final Exam
    Wednesday, June 3:
    • Topic: Review
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, June 1:
    • Topic: Principal Component Analysis and applications
      Introduction to principal component analysis (PCA) and applications, we will do face recognition and applications to analysis of data.
      • Reading Homework: Read Section 7.5 and watch the videos (due today at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 9
    Friday, May 29:
    • Topic: Applications to image processing
      Today we will discuss applications to image processing (different applications for Section 1 and 3 than Sect. 2)
    • WebWork Review (due Monday before class)
    • Reading Homework: There is no section in the book (due Monday at the beginning of class)
    • Suggested Homework: Suggested Written Homework: Sect. 7.4 # 7, 12, 15, 18 (This will not be collected)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, May 27:
    • Topic: The Singular Value Decomposition and applications
      Introduction to Singular Value Decomposition
    • WebWork Sec. 7.4 (due Friday before class)
      • Reading Homework: Read Section 7.4 and watch the videos (due today at the beginning of class)
    • Suggested Written Homework:7.4 # 7, 12, 15, 18 (This will not be collected)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, May 25:
    • Memorial Day! No classes.
    Week 8
    Friday, May 22:
    • Topic: The Page Rank Algorithm
      Today we give an application of Markov chains to search engines
    • WebWork Review (due Monday before class)
    • Reading Homework: There is no section in the book (due Monday at the beginning of class)
    • Written Homework: Homework Set #8 (due Wed. May 27 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, May 20:
    • Topic: Markov chains and the power method
      Today we will discuss the basics of Markov chains and the power method for approximating eigenvalues and eigenvectors.
    • WebWork Sec. 4.9 and 5.8 (due Friday before class)
      • Reading Homework: Read Section 4.9 and 5.8 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #8 (due Wed. May 27 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, May 18:
    • Topic: Orthogonally diagonalizable and symmetric matrices
      Today we discuss symmetric matrices and orthogonal diagonalization. Including the spectral decomposition theorem.
    • WebWork Sec. 7.1 (due Wednesday before class)
    • Reading Homework: Read Section 7.1 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 7
    Friday, May 15:
    • Topic: Orthogonal Projections and the Gram-Schmidt Process
      Today we will learn how to compute orthogonal bases.
    • WebWork Sec. 6.3 and 6.4 (due Monday before class)
    • Reading Homework: Read Sect. 6.3 and 6.4 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #7 (due Wed. May 20 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, May 13:
    • Topic: Orthogonal Projections
      Today we will be studying orthogonal projections
    • WebWork Sec. 6.2 and 6.3 (due Friday before class)
      • Reading Homework: Read Section 6.2 and 6.3 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #7 (due Wed. May 20 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, May 11:
    • Topic: The Inner Product, length and orthogonality
      Today we will be learning about the inner product and how this leads to definitions of length, distance, angle and orthogonality. We will define what it means for a basis to be orthogonal.
    • WebWork Sec. 6.1 (due Wednesday before class)
    • Reading Homework: Read Section 6.1 and 6.2 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 6
    Friday, May 8:
    • Topic: Diagonalization and connections to linear transformations.
      We will learn how to diagonalize a matrix and understands
    • WebWork Sec. 5.3 and 5.4 (due Monday before class)
    • Reading Homework: Read Sect. 5.3 and 5.4 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #6 (due Wed. May 13 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, May 6:
    • Topic: The characteristic equation and the characteristic polynomial of a matrix. We will learn about similar matrices and how it connects to the problem of finding eigenvalues and eigenvectors.
      We will learn how to compute the eigenvalues and about multiplicities of eigenvalues.
    • WebWork Sec. 5.2 (due Friday before class)
      • Reading Homework: Read Section 5.2 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #6 (due Wed. May 13 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, May 4:
    • Topic: Computing the Eigenvectors of a matrix
      Today we will be learning how to compute the eigenvectors when we are given the eigenvectors. We will also show that eigenvectors corresponding to distinct eigenvalues are linearly independent.
    • WebWork Sec. 5.1 (due Wednesday before class)
    • Reading Homework: Read Section 5.1 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 5
    Friday, May 1:
    • Topic: The determinant of a matrix and its properties
      We will describe two ways to compute the determinant of a matrix and study its properties.
    • WebWork Sec. 3.1 and 3.2 (due Monday before class)
    • Reading Homework: Read Sect. 3.1 and 3.2 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #5 (due Wed. May 6 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, April 29:
    • Topic: Matrix of a linear transformation, change of coordinates matrix and the matrix of the composition of linear tranformations.
      We will continue the discussion from Monday, we will learn how to compute the change of coordinates matrix and the matrix of the composition.
    • WebWork Sec. 4.7 and 5.4 (due Friday before class)
      • Reading Homework: Read Section 4.7 and 5.4 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #5 (due Wed. May 6 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 27:
    • Topic: The matrix of a linear transformation T : V --> W and the change of coordinates Matrix.
      We will define an m x n matrix for any linear tranformation from an n-dimensional vector space V to an m-dimensional vector space W. We will obtain the change of coordinates matrix as a special case when T is the identity transformation.
    • WebWork Sec.4.4 and 5.4 (due Wednesday before class)
    • Reading Homework: Read Section 4.4, 4.7 and 5.4 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 4
    Friday, April 24:
    • Topic: Coordinates, dimension and rank of a matrix
      Today we will introduce the concept of coordinates and define the dimension of a vector space, and the rank of a matrix.
    • WebWork Sec. 2.9 (due Monday before class)
    • Reading Homework: Read Sect. 2.9 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #4 (due Wed. April 29 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, April 22:
    • Topic: Basis of a vector space
      We will discuss linear independent sets for general vector spaces, the definition of a basis, how to find a basis from a spanning set. We will also learn how to compute bases for Col A and Nul A.
    • WebWork Sec. 4.3 (due Friday before class)
      • Reading Homework: Read Section 4.3 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #4 (due Wed. April 29 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 20:
    • Topic: Inverse Matrix Theorem and the inverse of a linear transformation.
      We will discuss the Inverse Matrix Theorem (IMT) and discuss connections of matrices to linear transformations, in particular how the inverse is connected to the inverse of its standard matrix.
    • WebWork Sec. 2.3 (due Wednesday before class)
    • Reading Homework: Read Section 2.3 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 3
    Friday, April 17:
    • Topic: Inverse of a Matrix
      Today we will learn an algorithm for finding the inverse of a matrix based on the elementary row operations. We will also see that elementary row operations have matrix representations. We will also discuss the linear system Ax=b when A is invertible.
    • WebWork Sec. 2.1 (due Monday before class)
    • Reading Homework: Read Sect. 2.1 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #3 (due Wed. April 22 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, April 15:
    • Topic: one-to-one and onto linear transformations and Matrix operations
      Today we will study one-to-one and onto linear trasformations and see how this connects to the fundamental questions that we have been discussing in class.
    • WebWork Sec. 1.9 and 2.1 (due Friday before class)
      • Reading Homework: Read Section 1.9 and 2.1 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #3 (due Wed. April 22 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 13:
    • Topic: Linear Transformations
      Today we will learn about linear transformations, the kernel and the range and how these relate to Nul A and Col A for a matrix A.
    • WebWork Sec. 4.2 and 1.9 (due Wednesday before class)
    • Reading Homework: Read Section 4.2 and 1.9 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 2
    Friday, April 10:
    • Topic: Introduction to Vector Spaces, null space, column space.
      Today we will learn the general framework for what we have been doing. This will help us apply more general theorems and get a better understanding of what we have been doing.
    • WebWork Sec. 4.1 and 4.2 (due Monday before class)
    • Reading Homework: Read Sect. 4.1 and 4.2 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #2 (due Wed. April 15 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, April 8:
    • Topic: Linear Independence
      Today we will learn about linear independent sets and connections to linear systems.
    • WebWork Sec. 1.7 (due Friday before class)
      • Reading Homework: Read Section 1.7 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #2 (due Wed. April 15 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 6:
    • Topic: The Matrix Equation Ax=b and its solutions
      Today we will continue discussing the matrix equation Ax=b and introduce homogeneous systems and relate solutions to homogeneous systems to solutions of Ax=b in general.
    • WebWork Sec. 1.4 and 1.5 (due Wednesday before class)
    • Reading Homework: Read Section 1.4 and 1.5 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 1
    Friday, April 3:
    • Topic: Vector Equations; Matrix Equations
      Today we will learn how to interpret a system of linear equations both as a vector equation or as a matrix equation.
    • WebWork Sec. 1.3 and 1.4 (due Monday before class)
    • Reading Homework: Read Sect. 1.3 and 1.4 and watch the videos (due Monday at the beginning of class)
    • Written Homework: Homework Set #1 (due Wed. April 8 at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, April 1:
    • Topic: Row Reduction and Echelon Forms
      Today we will learn about solving systems of linear equations and converting one system to another system with the same solution set.
    • WebWork Sec. 1.2 (due Friday before class)
      • Reading Homework: Read Section 1.2 and watch the videos (due Friday at the beginning of class)
    • Written Homework: Homework Set #1 (due Wed. April 8 at the beginning of class or before)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, March 30:
    • Topic: Linear Systems of Equations
      Today we will have an introduction to the course as well as introduce systems of linear equations and solutions to these systems.
    • WebWork Sec. 1.1 (due Wednesday before class)
    • Reading Homework: Read Section 1.1 and watch the videos (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.


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