**To read:**All of the Introduction and Section 2.1, Section 2.2 through Example 4.**Be sure to understand:**In Section 2.1, the section "Matrix Multiplication" and Example 3; in Section 2.2, the statement of Theorem 5.- If A is a 10 x 7 matrix and B is a 2 x 10 matrix, does AB exist, and if so, how many columns does it have? How about BA?
- Give one way in which matrix multiplication differs from multiplication of real numbers.
- Suppose A is an invertible matrix. Can A
**x**=**b**have infinitely many solutions? - You will be receiving the take-home exam Monday in class. Make sure you have copies of all group homework {\em before} then, as asking for a particular homework from a colleague becomes problematical (that is, open to interpretation as being dishonourable) once you have the exam in your possession.
**To read:**Finish Section 2.2, read all of Section 2.3.**Be sure to understand:**In Section 2.2, the statement of Theorem 7; in Section 2.3, the statement of Theorem 8.- Find the inverse of the matrix A defined as . Use Maple notation to write the result.
- Suppose A=[
**u**,**v**,**w**] is invertible. What is span{**u**,**v**,**w**}? - In Example 2 in Section 2.3, how do we know that T maps
**R**^{n}*onto***R**?^{n} - Following the honor code regarding the take home exam means not discussing the exam
*at all*with anybody but me. - Don't put off working on the exam. (I give you four days for a reason!)
- Come to me with questions -- but only after you really have thought about the question and looked through your book, notes, and homework for ideas!
**To read:**Review Sections 1.7 through 2.3. (Presumably, you are anyway, for the exam)**Be sure to understand:**Try to see the big picture, the connections betweeen the ideas.**To read:**The section "Difference Equations" in Section 1.9 and all of Section 4.9.**Be sure to understand:**The section "Predicting the Distant Future" in Section 4.9- What is the point of studying Markov chains?
**To read:**Re-read**Be sure to understand:**Understand more deeply- What is a steady state vector for a stochastic matrix P?
- What is special about
*regular*stochastic matrices? **To read:**Through the section "Homogeneous 3D Coordinates"**Be sure to understand:**Examples 4, 5, and 6- What is the advantage of using homogeneous coordinates in computer graphics?
**To read:**All**Be sure to understand:**The definition of determinant, and the statements of Theorems 3, 4, and 6- Why do we care about finding det(A)?
- If A=, what is det(A)?
**To read:**Review Sections 1.9, 4.9, 2.8, 3.1 and 3.2

**Be sure to understand:**Deeper connections than you did the first time around- Write a
*brief*summary of Sections 3.1 and 3.2. Focus on the big ideas and the connections between them. **To read:**All**Be sure to understand:**The definition of a vector space and a subspace, Examples 4 and 8, and the statement of Theorem 1- Is the subset of
**R**consisting of all scalar multiples of the vector (5, 6, -3) a subspace of^{3}**R**? Why or why not?^{3} - Give an example of a subset of
**R**that is not a subspace of^{2}**R**?^{2} **To read:**All**Be sure to understand:**The section "The Contrast between Nul A and Col A"- True or False: If A is a 3 x 5 matrix, then Nul A and Col A are subspaces of
**R**^{3} - Let A=. Find Nul A.
**To read:**All**Be sure to understand:**The definition of a basis, Theorem 5, and the section "Two Views of a Basis"- Let
**v**=(1,2),_{1}**v**=(3,4), and_{2}**v**=(4,6). Give a basis for H=Span{_{3}**v**,_{1}**v**,_{2}**v**}._{3} - If A is a 4 x 5 matrix with three pivot positions, how many vectors does a basis for Col A contain?
**To read:**Review Sections 4.1 through 4.3**Be sure to understand:**Get a deeper understanding of the ideas than you had before- Write a
*brief*summary of Sections 4.1 through 4.3. As always, focus on the big ideas and the relationship between them. **To read:**All**Be sure to understand:**Theorems 10, 11, and 12- What is the dimension of
**R**? Why? Does this make sense geometrically?^{3} - Can there be a set of linearly independent vectors {
**v**,_{1}**v**, ...,_{2}**v**} that does not span_{1}**R**? Explain.^{12}

Fall 2001, Math 221

**October 2001**

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 Monday 10/1 at 8am__

**Introduction to Chapter 2**

**Section 2.1: Matrix Operations**

**Section 2.2 : The Inverse of a Matrix**

**E-mail Subject Line:** Math 221 Your Name 10/1

**Reading questions:**

**Reminder:**

__ Due Wednesday 10/3 at 8am__

**Section 2.2 : The Inverse of a Matrix**

**Section 2.3: Characterization of Invertible Matrices**

**E-mail Subject Line:<**

Math 221 Your Name 10/3

**Reading Questions:**

**Reminder:**

__ Due Friday 10/5 at 8am__

**The Big Picture**

**Exam 1 Due Today. No Reading Questions**

__Monday 10/8: Enjoy your Fall Break!__

__ Due Wednesday 10/10 at 8am__

**Section 1.9: Linear Models in Business, Science, and Engineering**

**Section 4.9: Applications to Markov Chains**

**E-mail Subject Line:** Math 221 Your Name 10/10

**Reading questions:**

__ Due Friday 10/12 at 8am__

**Section 1.9: Linear Models in Business, Science, and Engineering**

**Section 4.9: Applications to Markov Chains**

**E-mail Subject Line:** Math 221 Your Name 10/12

**Reading questions:**

__ Due Monday 10/15 at 8am__

**Section 2.8: Applications to Computer Graphics**

**E-mail Subject Line:** Math 221 Your Name 10/15

**Reading questions:**

__ Due Wednesday 10/17 at 8am__

**Introduction to Chapter 3**

**Section 3.1: Introduction to Determinants**

**Section 3.2: Properties of Determinants**

**E-mail Subject Line:** Math 221 Your Name 10/17

**Reading questions:**

__ Due Friday 10/19 at 8am__

**The Big Picture**

**E-mail Subject Line:** Math 221 Your Name 10/19

**Reading questions:**

__ Due Friday 10/22 at 8am__

**Introduction to Chapter 4**

**Section 4.1: Vector Spaces and Subspaces**

**E-mail Subject Line:** Math 221 Your Name 10/22

**Reading questions:**

__ Due Wednesday 10/24 at 8am__

**Section 4.2: Null Spaces, Column Spaces, and Linear Transformations**

**E-mail Subject Line:** Math 221 Your Name 10/24

**Reading questions:**

__ Due Friday 10/26 at 8am__

**Section 4.3: Linearly Independent Sets; Bases**

**E-mail Subject Line:** Math 221 Your Name 10/26

**Reading questions:**

__ Due Monday 10/29 at 8am__

**The Big Picture**

**E-mail Subject Line:** Math 221 Your Name 10/29

**Reading Questions:**

__ Due Wednesday 10/31 at 8am__

**Section 4.5**

**E-mail Subject Line:** Math 221 Your Name 10/31

**Reading questions:**

Go to the reading assignments for November!

Department of Mathematics and Computer Science

Science Center, Room 109

Norton, Massachusetts 02766-0930

TEL (508) 286-3973

FAX (508) 285-8278

jsklensk@wheatonma.edu

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