I'll use Maple syntax for mathematical notation on this page.
All section and page numbers refer to sections from Lay, updated 2nd edition.

Due Friday 11/2 at 8am

Section 4.6: Rank
Introduction to Chapter 5
Section 5.1: Eigenvectors and Eigenvalues

• To read: All of Section 4.6 and the Intro to Ch. 5. Through Example 3 in Section 5.1.
• Be sure to understand: In Section 4.6, the definition of rank, the Rank Theorem, and the continuation of the Invertible Matrix Theorem. In Section 5.1, the definitions of eigenvector and eigenvalue, and Example 3.

E-mail Subject Line: Math 221 Your Name 11/2

Reading Questions:

1. If A is a 4 x 7 matrix with three pivots, what is the dimension of Nul A? Why?
2. Let A= . Verify that (1, -2) is an eigenvector of A with corresponding eigenvalue 3.

Due Monday 11/5 at 8am

Section 5.1: Eigenvectors and Eigenvalues

• To read: Finish
• Be sure to understand: Example 4

E-mail Subject Line: Math 221 Your Name 11/5

Reading questions:

Suppose A is a 3 x 3 matrix with eigenvalues 1, 2, and 5.
1. What is the dimension of Nul(A)?
2. What is the dimension of the eigenspace of A?

Due Wednesday 11/7 at 8am

Section 5.2: The Characteristic Equation

• To read: All. The section on determinants will be review.
• Be sure to understand: The definition of the characteristic equation, Example 3, and the definition of similarity.

E-mail Subject Line: Math 221 Your Name 11/7

Reading questions:

1. Let A=. Find the characteristic equation of A.
2. How is the characteristic equation of a matrix related to the eigenvalues of t he matrix?

Due Friday 11/9 at 8am

The Big Picture

• To read: Review Sections 4.5, 4.6, 5.1, 5.2
• Be sure to understand: Try to see the big picture, the connections betweeen the ideas.

E-mail Subject Line: Math 221 Your Name 11/9

Reading questions:

1. Write a brief summary of these four sections. As usual, focus on the big ideas and the relationships between them.

Due Monday 11/12 at 8am

Section 5.3: Diagonalization

• To read: All
• Be sure to understand: Example 3

E-mail Subject Line: Math 221 Your Name 11/12

Reading questions:

1. What is the point of finding a diagonalization of a matrix?
2. If A is 4x4 with eigenvalues 1, 2, 0, 3, is A diagonalizable? Explain.

Due Wednesday 11/14 at 8am

Section 5.6: Discrete Dynamical Systems

• To read: Through Example 4
• Be sure to understand: Example 1, and the plots in Examples 2, 3 , and 4

E-mail Subject Line: Math 221 Your Name 11/14

Reading questions:

1. Let A = . Determine whether the origin is an attractor, a repellor, or a saddle point for solutions to x_k+1=Ax_k.

Reminders:

• You probably don't need reminding, but don't put off working on Exam 2.

Due Friday 11/16 at 8am

Section 6.1: Inner Product, Length, and Orthogonality

• To read: All
• Be sure to understand: The definitions of inner product, norm, and orthogonal complement

Exam 2 due today. No reading questions.

Due Monday 11/19 at 8am

The Big Picture

• To read: Review Sections 5.3, 5.6, 6.1. (You may have already done most of this while taking the exam.)
• Be sure to understand: The big picture, the connections between ideas.

E-mail Subject Line: Math 221 Your Name 11/19

Reading questions:

1. Write a brief summary of Section 6.1. Focus on the big ideas, and the connections between them (and the connections between the new ideas and old ones.)

Due Monday 11/26 at 8am

Section 6.2: Orthogonal Sets

• To read: Through the section "Decomposing a Force into Component Forces"
• Be sure to understand: The statement of Theorem 4 and Figure 4

E-mail Subject Line: Math 221 Your Name 11/26

Reading questions:

1. Give an example of an orthogonal basis for R³.
2. Let w be the orthogonal projection of y onto u. What direction does w point? What direction does y-w point?

Due Wednesday 11/28 at 8am

Section 6.3: Orthogonal Projections

• To read: Through Example 3
• Be sure to understand: Figure 2 and the statement of the Best Approximation Theorem

E-mail Subject Line: Math 221 Your Name 11/28

Reading questions:

Let y=(1, 2, 3) in R³ and let W be the xz-plane.
1. What is the orthogonal projection of y onto W?
2. Is there a point in W that is closer to y than the orthogonal projection you just found? Why or why not?

Due Friday 11/30 at 8am

Section 6.3: Orthogonal Projections

• To read: Through Example 3
• Be sure to understand: Figure 2 and the statement of the Best Approximation Theorem

E-mail Subject Line: Math 221 Your Name 11/28

Reading questions:

Let y=(1, 2, 3) in R³ and let W be the xz-plane.
1. What is the orthogonal projection of y onto W?
2. Is there a point in W that is closer to y than the orthogonal projection you just found? Why or why not?