Math 22: Linear Algebra with Applications

Winter 2025

Homework Assignments


  • 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

  • Late Homework will not be accepted. If you must miss a class, it is your responsibility to submit all homework on time.
  • Make sure that in your homework you indicate everyone that helped you in the homework or anyone with whom you collaborated. For example, write "Tutorial" or "Office Hours", if you received help from these sources.

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

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

    Week 6
    Friday, February 14:
    • Topic: Diagonalization and connections to linear transformations.
      We will learn how to diagonalize a matrix and understand how this is a factorization problem. We will also make connections to linear transformations.
    • WebWork Sec. 5.3 and 5.4 (due Monday at 10pm)
    • Reading Homework: Read Sect. 6.1 and 6.2 (due Monday at the beginning of class)
    • Written Homework: Homework Set #6 (due Tues. February 18 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, February 12:
    • Topic: The characteristic equation and the characteristic polynomial of a matrix.
      We will learn how to compute the eigenvalues and the definition of similar matrices. And how similar matrices connect 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 at 10pm)
      • Reading Homework: Read Section 5.3 and 5.4 (due Friday at the beginning of class)
    • Written Homework: Homework Set #6 (due Tues. February 18 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, February 10:
    • Topic: Eigenvalues, Eigenvectors and Eigenspaces
      Today we will be learning how to compute the eigenvectors when we are given the eigenvalues. We will also show that eigenvectors corresponding to distinct eigenvalues are linearly independent.
    • WebWork Sec. 5.1 (due Wednesday at 10pm)
    • Reading Homework: Read Section 5.2 and watch the videos (due Wednesday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 5
    Friday, February 7:
    • 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 10PM)
    • Reading Homework: Read Sect. 5.1 and 5.2 (due Monday at the beginning of class)
    • Written Homework: Homework Set #5 (due Tues. February 11 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, February 5:
    • 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 10PM)
      • Reading Homework: Read Section 3.1 and 3.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #5 (due Tues. February 11 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, February 3:
    • 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 10PM)
    • Reading Homework: Read Section 4.4, 4.7 and 5.4 (due Wednesday at the beginning of class )
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 4
    Friday, January 31:
    • Topic: Coordinates, Dimension, and Rank
      Sec. 2.9 Coordinates, dimension and rank Today we define the coordinate map, define dimension and rank.
    • WebWork Sec. 2.9 (due Monday at 10PM)
    • Reading Homework: Read Sect. 4.4, 4.7 and 5.4 (due Monday at the beginning of class)
    • Written Homework: Homework Set #4 (due Tues. February 4 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Thursday, January 30:
    • Midterm #1 in Wilder 104, 7:00 - 9:00 PM.
    Wednesday, January 29:
    • Topic: Linear independent sets and bases
      Sec. 4.3
      Today we discuss linear independent sets for any vector space and define bases for any vector space. We discuss how to get bases from spanning sets and how to compute bases for Nul A and Col A.
    • WebWork Sec. and 4.3 (due Friday before class)
      • Reading Homework: Read Section 2.9 (due Friday at the beginning of class)
    • Written Homework: Homework Set #4 (due Tues. February 4 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, January 27:
    • Topic: Inverse Matrix Theorem and connections to linear transformations
      Sec. 2.3: Today we learn the Inverse Matrix Theorem (IMT) we discuss the composition of linear transformations, define the inverse of an invertible linear transformation.
    • WebWork Sec. 2.3 (due Wednesday 10PM)
    • Reading Homework: Read Section 4.3 (due Wednesday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 3
    Friday, January 24:
    • Topic: Inverse of a Matrix
      Sec. 2.2 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 by 10PM)
    • Reading Homework: Read Sect. 2.3 (due Monday at the beginning of class)
    • Written Homework: Homework Set #3 (due Tues. January 28 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, January 22:
    • Topic: One-to-one and onto linear transformations and Matrix operations
      Sec. 1.9 and 2.1
      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. and 2.1 (due Friday by 10PM)
      • Reading Homework: Read Section 2.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #3 (due Tues. January 28 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, January 20 (moved to x-hour due to MLK):
    • Topic: Linear Transformations
      Sec. 4.2 and 1.9: Today we will learn about linear transformations, the kernel and the range of a linear transformation and how these relate to Nul A and Col A for a matrix A.
    • WebWork Sec. 4.2 and 1.9 (due Wednesday by 10PM)
    • Reading Homework: Read Section 1.9 and 2.1 (due Monday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Week 2
    Friday, January 17:
    • 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 at 10PM)
    • Reading Homework: Read Sect. 4.2 and 1.9 (due Monday at the beginning of class)
    • Written Homework: Homework Set #2 (due Tues. January 21 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, January 15:
    • Topic: Linear Independence
      Today we will learn about linear independent sets and connections to linear systems.
    • WebWork Sec. 1.7 (due Friday by 10PM)
      • Reading Homework: Read Section 4.1-4.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #2 (due Tues. January 21 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, January 13:
    • 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 by 10PM)
    • Reading Homework: Read Section 1.7 (due at the beginning of class)
    Week 1
    Friday, January 10:
    • 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 by 10PM)
    • Reading Homework: Read Sect. 1.5 (due Monday at the beginning of class)
    • Written Homework: Homework Set #1 (due Tues. January 14 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Wednesday, January 8:
    • 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 by 10PM)
      • Reading Homework: Read Section 1.3-1.4 (due Friday at the beginning of class)
    • Written Homework: Homework Set #1 (due Tues. January 14 at 10PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, January 6:
    • 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 by 10PM)
    • Reading Homework: Read Section 1.1 and 1.2 (due Wednesday at the beginning of class)
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas (due Sunday by 10 PM).
    • If you are adding the class on January 6 or later, email your instructor to get access to WeBWork and Gradescope.


    Page created and maintained by R. Orellana