
Math 221  Linear Algebra  Reading Assignments
September 1999

Be sure to check back, because this may change during the semester.
Last modified:
Wednesday, August 18, 1999,
1:44 PM
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Linear Algebra and Its Applications by David Lay.
For September 14
Introduction to Chapter 1
Section 1.1 Systems of Linear Equations
Section 1.2 Row Reduction and Echelon Forms
 To read : All
 Be sure to understand : Example 2 in 1.1, the section "Existence and Uniqueness Questions" in 1.2
Email Subject Line : Math 221 9/14 Your Name
Reading Questions :
Let A be the matrix
 Is A is row echelon form? Why or why not?
 What values are in the pivot positions of A?
 Suppose that A is the augmented matrix for a system of 3 equations in 3 unknowns. Is the system consistent or inconsistent? Explain.
For September 16
Section 1.3 Vector Equations
 To read : All
 Be sure to understand : The section "Linear Combinations"
and the definition of Span{u,v}
Email Subject Line : Math 221 9/16 Your Name
Reading Questions :
 Let y=(1,2,3), u=(1,0,0) and v=(0,4,6). 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}.
For September 21
Section 1.4 The Matrix Equation Ax=b
Section 1.5 Solution Sets of Linear Systems
 To read : All
 Be sure to understand : The statement of Theorem 4 in 1.4, Example 3 and the statement of Theorem 6 in 1.5
Email Subject Line : Math 221 9/21 Your Name
Reading Questions :
 Suppose A is a 4x5 matrix with 3 pivots. Do the columns of A span R^{4}?
 Explain the difference between a homogeneous system of equations and a nonhomogeneous system of equations.
 If the system Ax=b is consistent and Ax=0 has a
nontrivial solution, how many solutions does Ax=b have?
For September 23
Section 1.6 Linear Independence
 To read : All
 Be sure to understand : The section "Linear Independence of Matrix Columns"
Email Subject Line : Math 221 9/23 Your Name
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} cannot be linearly independent.
For September 28
Section 1.7 Introduction to Linear Transformations
 To read : All
 Be sure to understand : Example 1, the definition of a linear transformation
Email Subject Line : Math 221 9/28 Your Name
Reading Questions :
 Let T:R^{2} > R^{2} be a transformation defined by
T(x_{1}, x_{2}) = (x_{1}+2, x_{2} + 3). Is T a
linear transformation? (Hint: Look at Property 3)
 If T:R^{5} > R^{3} is a linear transformation
where Tx=Ax, what is the size of the matrix A?
For September 30
Section 1.8 The Matrix of a Linear Transformation
 To read : All
 Be sure to understand : Examples 1 and 2, the definition of oneone and onto, the statement of Theorems 11 and 12
Email Subject Line : Math 221 9/30 Your Name
Reading Questions :
 Give the matrix A for the linear transformation
T:R^{2} > R^{2} that expands horizontally by a factor of 2.
 Let T:R^{5} > R^{3} be a linear transformation with
standard matrix A where A has three pivots. Is T oneone? Explain.
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