
Math 221  Linear Algebra  Reading Assignments
November 1999

Be sure to check back, since these may change.
(Last modified:
Wednesday, August 18, 1999,
3:32 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 November 2
Reread Section 4.3, but no Reading Questions for today.
For November 4
Section 4.5 The Dimension of a Vector Space
Section 4.6 Rank
 To read : All
 Be sure to understand : Theorems 10, 11, and 12 in 4.5
and the definition of rank, the Rank Theorem, the
continuation of the Invertible Matrix Theorem in 4.6
Email Subject Line : Math 221 11/4 Your Name
Reading Questions :
 What is the dimension of R^{3}? Why? Does this make sense geometrically?
 Can there be a set of linearly independent vectors
{v_{1},v_{2},. . ., v_{12}}
that does not span R^{12}? Explain.
 If A is 4x7 with three pivots, what is the dimension of Nul A? Why?
For November 9
Section 5.1 Eigenvectors and Eigenvalues
 To read : All
 Be sure to understand : The definitions of eigenvector and eigenvalue,
and Examples 3 and 4
Email Subject Line : Math 221 11/9 Your Name
Reading Questions:
 Let A=.
Verify that (1,2) is an eigevector of A with corresponding eigenvalue 3.
 Suppose A is 3x3 with eigenvalues 1, 2, and 5. What is the dimension of
nul(A)?
For November 11
Section 5.2 The Characteristic Equation
 To read : All, but the section on Determinants should be review
 Be sure to understand : The definition of the characteristic equation, Example 3, and the definition of similarity
Email Subject Line : Math 221 11/11 Your Name
Reading Questions:
 Let A=.
Find the characteristic equation of A.
 How is the characteristic equation of a matrix related to the eigenvalues of the matrix?
For November 16
Section 5.3 Diagonalization
 To read : All
 Be sure to understand : Example 3
Email Subject Line : Math 221 11/16 Your Name
Reading Questions:
 What is the point of finding a diagonalization of a matrix?
 If A is 4x4 with eigenvalues 1, 2, 0, 3, is A diagonalizable? Explain.
For November 18
Section 5.6 Discrete Dynamical Systems
 To read : Through Example 4
 Be sure to understand : Example 1 and the plots in Examples 2, 3, and 4
Exam 2 due today. No Reading Questions.
For November 23
Section 6.1 Inner Product, Length, and Orthogonality
 To read : All
 Be sure to understand : The definitions of the inner product, norm, and orthogonal complement
Email Subject Line : Math 221 11/23 Your Name
Reading Questions :
 Are the two vectors u=(3,1) and v=(2,3) in R^{2} orthogonal? Why or why not?
 Let W be the xzplane in R^{3}. What is the orthogonal complement of W?
For November 25
Thanksgiving Break.
For November 30
Section 6.2 Orthogonal Sets
 To read : Through the section "Decomposing a Force into Component Forces"
 Be sure to understand : The statement of Theorem 4 and Figure 4
Email Subject Line : Math 221 11/30 Your Name
Reading Questions :
 Give an example of an orthogonal basis for R^{3}.
 Let w be the orthogonal projection of y onto u.
What direction does w point? What direction does y  w point?
Math 221 Home 
T. Ratliff's Home
