Reading Assignments for Linear Algebra
Fall 2001, Math 221
September 2001
Be sure to check back often, because assignments may change!
Last modified: 9/25/01
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 9/7, at 8am
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Introduction to Chapter 1
Section 1.1: Systems of Linear Equations
Section 1.2: Row Reduction and Echelon Form
- To read: All
- Be sure to understand Example 2 in 1.1; the section "Existence and Uniqueness Questions" in Section 1.2.
E-mail Subject Line: Math 221 Your Name 9/7
Reading questions:
Let A be the matrix
- Is A in row echelon form? Why or why not?
- What values are in the pivot positions of A?
- Suppose that A i sthe augmented matrix for a system of 3 equations in 3 unknowns. Is the system consistent or inconsistent? Explain.
Due Monday 9/10 at 8am
Section 1.3 : Vector Equations
- To read:
All
- Be sure to understand:
The section "Linear Combinations" and the definition of Span{u,v}
E-mail Subject Line: Math 221 Your Name 9/10
Reading questions:
- Let y=(4,9,3), u=(0,1,0), and v=(12,0,9). Write y as a linear combination of u and v.
- Let u=(1,0,0) and v=(0,1,0). Give a geometric description of Span{u,v}.
Due Wednesday 9/12 at 8am
Section 1.4: The Matrx Equation Ax=b
- To read:
All
- Be sure to understand:
The statement of Theorem 4
E-mail Subject Line: Math 221 Your Name 9/12
Reading questions:
- Suppose A is a 4x5 matrix with 3 pivots. Do the columns of A span R^{4}?
- Simplify
Due Friday 9/14 at 8am
Section 1.5: Solution Sets of Linear Systems
- To read:
All
- Be sure to understand:
Example 3 and the statement of Theorem 6
E-mail Subject Line: Math 221 Your Name 9/14
Reading questions:
- Explain the difference between a homogeneous system of equations and a non-homogeneous system of equations.
- If the system Ax=b is consistent and Ax=0 has a non-trivial solution, how many solutions does Ax=b have?
Due Monday 9/17 at 8am
Linear Independence
- To read:
All
- Be sure to understand:
The section "Linear Independence of Matrix Columns"
E-mail Subject Line: Math 221 Your Name 9/17
Reading questions:
- If Ax=0 has infinitely many solutions, can the columns of A be linearly independent? Explain.
- If Ax=b has infinitely many solutions, can the columns of A be linearly independent? Explain.
- Explain in your own words why a set of three vectors in R^{2} can not be linearly independent.
Reminder:
- On Monday 9/24 at 5pm, Gregory Rawlins will be giving the Johnson lecture Why Napster Doesn't Matter:
Intellectual Property in the Age of Piracy. This is a required part of the course, so make sure it's in your schedule.
Due Wednesday 9/19 at 8am
The Big Picture
- To read:
Review Sections 1.1 through 1.6
- Be sure to understand:
The big ideas and the deeper connections that you may have missed the first time around
E-mail Subject Line: Math 221 Your Name 9/19
Reading questions:
- Write a brief summary of Sections 1 through 6. It should be short (I don't intend this to take you more than 15 minutes after you finish reviewing), and should focus on the big ideas and the relationships between those ideas.
Due Friday 9/21 at 8am
Section 1.7: Introduction to Linear Transformations
- To read:
Through Example 3
- Be sure to understand:
Example 1
E-mail Subject Line: Math 221 Your Name 9/21
Reading questions:
Let A be the matrix , and let T:R^{2} --> R^{2} be defined by T(x)=Ax.
- Find T(-4,10).
- Is (4,-2) in the range of T?
Due Monday 9/24 at 8am
Section 1.7: Introduction to Linear Transformations
- To read:
Finish
- Be sure to understand:
The definition of a linear transformation
E-mail Subject Line: Math 221 Your Name 9/24
Reading Questions:
- Let T:R^{2} --> R^{2} be a transformation defined by T(x_{1}, x_{2})=(x_{2}-3, 4x_{1}+10). Is T a linear transformation?
- If T:R^{5} --> R^{3} is a linear transformation where T(x)=Ax, what is the size of the matrix A?
Reminder:
- Sadly, the Johnson lecture has been postponed indefinitely
Due Wednesday 9/26 at 8am
Section 1.8: The Matrix of a Linear Transformation
- To read:
All
- Be sure to understand:
Examples 1 and 2, the definition of one-to-one and onto, the statement of Theorems 11 and 12
E-mail Subject Line: Math 221 Your Name 9/26
Reading questions:
- Give the matrix A for the linear transformation T: R^{2} --> R^{2} that rotates the plane by Pi/4 degrees counter-clockwise.
- Give the matrix A for the linear transformation T:R^{2} --> R^{2} that expands horizontally by a factor of 2.
Due Friday 9/28 at 8am
Section 1.8: The Matrix of a Linear Transformation
- To read:
Re-read it all. Especially focus on the definitions of one-to-one and onto, and on the specific results relating to linear transformations that are one-to-one or onto.
- Be sure to understand:
The concepts of one-to-one and onto.
E-mail Subject Line: Math 221 Your Name 9/28
Reading questions:
Let T:R^{5} --> R^{3} be a linear transformation with standard matrix A, where A has three pivots.
- Is T one-to-one?
- Is T onto?
Here ends the reading for September
Go to the reading assignments for October!
Janice Sklensky
Wheaton College
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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