
Math 221  Linear Algebra  Reading Assignments
October 1999

Be sure to check back, since these may change.
Last modified:
Thursday, August 19, 1999,
12:51 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 October 5
Introduction to Chapter 2
Section 2.1 Matrix Operations
Section 2.2 The Inverse of a Matrix
 To read : All
 Be sure to understand : The section "Matrix Multiplication" and Example 3 in 2.1, the statement of Theorems 5 and 7 in 2.2
Email Subject Line : Math 221 10/5 Your Name
Reading Questions :
 Give one way in which matrix multiplication differs from multiplication of real numbers.
 Suppose A is invertible. Can Ax=b have infinitely many solutions?
For October 7
Section 2.3 Characterizations of Invertible Matrices
 To read : All
 Be sure to understand : The statement of Theorem 8
Reading Questions : Exam 1 due today. No Reading Questions.
For October 13
Fall Break  No Reading Assignment
For October 14
Section 1.9 Linear Models in Business, Science, and Engineering
Section 4.9 Applications to Markov Chains
 To read : The section "Difference Equations" in 1.9 and all of 4.9
 Be sure to understand : The section "Predicting the Distant Future" in 4.9
Email Subject Line : Math 221 10/14 Your Name
Reading Questions:
 What is the point of studying Markov chains?
 What is a steady state vector for a stochastic matrix P?
 What is special about regular stochastic matrices?
For October 19
Section 2.8 Applications to Computer Graphics
 To read : Thru the section "Homogeneous 3D Coordinates"
 Be sure to understand : Examples 4, 5, and 6.
Email Subject Line : Math 221 10/19 Your Name
Reading Question:
What is the advantage of using homogeneous coordinates in computer graphics?
For October 21
Introduction to Chapter 3
Section 3.1 Introduction to Determinants
Section 3.2 Properties of Determinants
 To read : All
 Be sure to understand : The definition of the determinant, and the statements of Theorems 3, 4, and 6
Email Subject Line : Math 221 10/21 Your Name
Reading Questions :
 Why do we care about finding det(A)?
 If A = ,
what is det(A)?
For October 26
Introduction to Chapter 4
Section 4.1 Vector Spaces and Subspaces
Section 4.2 Null Spaces, Column Spaces, and Linear Transformations
 To read : All, but you can skip Examples 2, 3, and 5 in 4.1
 Be sure to understand : The definition of a vector space, Examples 4 and 8
in Section 4.1, the definition of a subspace, the statement of Theorem 1, and the section "The Contrast Between Nul A and Col A" in Section 4.2
Email Subject Line : Math 221 10/26 Your Name
Reading Questions :
 Give an example of a subset of R^{2} that is not a subspace of
R^{2}.
 True or false: If A is a 3 x 5 matrix, then the nullspace and column space
of A are subspaces of R^{3}.
For October 28
Section 4.3 Linearly Independent Sets; Bases
 To read : All
 Be sure to understand : Definition of a basis, Theorem 5, and the section "Two Views of a Basis"
Email Subject Line : Math 221 10/28 Your Name
Reading Questions :
 Let v_{1}=(1,2), v_{2}=(3,4),
and v_{3}=(4,6). Give a basis for H=Span{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?
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