Math 22: Linear Algebra with Applications

Spring 2026

Homework Assignments


  • The latest homework will always appear on top.

  • 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 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 11PM)
    • Reading Homework: Read Sect. 5.1 and 5.2 (due Monday at the beginning of class)
    • Written Homework: Homework Set #5 (due Tues. May 5 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • 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 #14 Sec. 4.7 and 5.4 (due Friday 11PM)
      • Reading Homework: Read Section 3.1 and 3.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #5 (due Tues. May 5 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • 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 #13 Sec.4.4 and 5.4 (due Wednesday 11PM)
    • 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, April 24:
    • Topic: Coordinates, Dimension, and Rank
      Sec. 2.9 Coordinates, dimension and rank Today we define the coordinate map, define dimension and rank.
    • WebWork #12 Sec. 2.9 (due Monday at 11PM)
    • 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. April 28 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Thursday, April 23:
    • Midterm #1 in Life Science 100 Oopik Auditorium at 7:00 - 9:00 PM.
    Wednesday, April 22
    • 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 #11 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. April 28 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 20
    • 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 #10 Sec. 2.3 (due Wednesday 11PM)
    • 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, April 17:
    • 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 #9 Sec. 2.1 (due Monday at 11PM)
    • Reading Homework: Read Sect. 2.3 (due Monday at the beginning of class)
    • Written Homework: Homework Set #3 (due Tues. April 21 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • 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
      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 #8 Sec. and 2.1 (due Friday at 11PM)
      • Reading Homework: Read Section 2.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #3 (due Tues. April 21 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • Discussion Homework: Make sure to visit and post in the Discussion page for Canvas.
    Monday, April 13:
    • 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 #7 Sec. 4.2 and 1.9 (due Wednesday at 11PM)
    • 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, 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 #6 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. April 14 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • 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 #5 Sec. 1.7 (due Friday by 11 PM)
      • Reading Homework: Read Section 4.1-4.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #2 (due Tues. April 14 at 11 PM EST or before)
      Submit the homework using Gradescope.
    • 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 #4 Sec. 1.4 and 1.5 (due Wednesday by 11 PM)
    • Reading Homework: Read Section 1.7 (due Wednesday at the beginning of class)
    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 3: Sec. 1.3 and 1.4 (due Monday by 11PM)
    • Reading Homework: Read Sect. 1.5 (due Monday at the beginning of class)
    • Written Homework: Homework Set #1 (due Tues. April 7 at 11PM EST or before)
    • 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 2: Sec. 1.2 (due Friday by 11PM)
      • Reading Homework: Read Section 1.3-1.4 (due Friday at the beginning of class)
    • Written Homework: Homework Set #1 (due Tues. April 7 at 11PM EST 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 1: Sec. 1.1 (due Wednesday by 11PM)
    • 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).


    Page created and maintained by R. Orellana