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

    E-mail Subject Line: Math 221 Your Name 9/7

    Reading questions:

      Let A be the matrix

    1. Is A in row echelon form? Why or why not?
    2. What values are in the pivot positions of A?
    3. 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

    E-mail Subject Line: Math 221 Your Name 9/10

    Reading questions:

    1. Let y=(4,9,3), u=(0,1,0), and v=(12,0,9). Write y as a linear combination of u and v.
    2. 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

    E-mail Subject Line: Math 221 Your Name 9/12

    Reading questions:

    1. Suppose A is a 4x5 matrix with 3 pivots. Do the columns of A span R4?
    2. Simplify



    Due Friday 9/14 at 8am

    Section 1.5: Solution Sets of Linear Systems

    E-mail Subject Line: Math 221 Your Name 9/14

    Reading questions:

    1. Explain the difference between a homogeneous system of equations and a non-homogeneous system of equations.
    2. 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

    E-mail Subject Line: Math 221 Your Name 9/17

    Reading questions:

    1. If Ax=0 has infinitely many solutions, can the columns of A be linearly independent? Explain.
    2. If Ax=b has infinitely many solutions, can the columns of A be linearly independent? Explain.
    3. Explain in your own words why a set of three vectors in R2 can not be linearly independent.

    Reminder:


    Due Wednesday 9/19 at 8am

    The Big Picture

    E-mail Subject Line: Math 221 Your Name 9/19

    Reading questions:

    1. 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

    E-mail Subject Line: Math 221 Your Name 9/21

    Reading questions:

      Let A be the matrix , and let T:R2 --> R2 be defined by T(x)=Ax.
    1. Find T(-4,10).
    2. Is (4,-2) in the range of T?


    Due Monday 9/24 at 8am

    Section 1.7: Introduction to Linear Transformations

    E-mail Subject Line: Math 221 Your Name 9/24

    Reading Questions:

    1. Let T:R2 --> R2 be a transformation defined by T(x1, x2)=(x2-3, 4x1+10). Is T a linear transformation?
    2. If T:R5 --> R3 is a linear transformation where T(x)=Ax, what is the size of the matrix A?

    Reminder:


    Due Wednesday 9/26 at 8am

    Section 1.8: The Matrix of a Linear Transformation

    E-mail Subject Line: Math 221 Your Name 9/26

    Reading questions:

    1. Give the matrix A for the linear transformation T: R2 --> R2 that rotates the plane by Pi/4 degrees counter-clockwise.
    2. Give the matrix A for the linear transformation T:R2 --> R2 that expands horizontally by a factor of 2.


    Due Friday 9/28 at 8am

    Section 1.8: The Matrix of a Linear Transformation

    E-mail Subject Line: Math 221 Your Name 9/28

    Reading questions:

      Let T:R5 --> R3 be a linear transformation with standard matrix A, where A has three pivots.
    1. Is T one-to-one?

    2. 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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