
Mathematics 227 Course Outline
Text: Linear Algebra, 2nd ed., (updated), Lay  Addison Wesley (ISBN 0201347741)
Study Guide (ISBN 0201648474)
Instructor: Alan Stein
<stein@math.uconn.edu>
This outline is tentative and subject to change.
Section
 Topic
 Exercises

1.1

Systems of Linear Equations

5, 6, 9, 10, 1922, 29, 30

1.2

Row Reduction and Echelon Forms

1, 2, 5, 6, 13, 14, 2124

1.3

Vector Equations

712, 21, 22, 31, 32

1.4

Matrix Equations

3, 4, 7, 8, 19, 20, 23, 24, 29, 30

1.5

Solution Sets of Linear Systems

1, 2, 7, 8, 13, 14, 21, 22, 25, 26

1.6

Linear Independence

2, 10, 14, 18, 27, 28

1.7

Linear Transformations

2, 6, 12, 14, 22  24

1.8

Matrix of a Linear Transformation

4, 12, 14, 22  24

2.1

Matrix Operations

2, 6, 10, 15, 16, 24

2.2

Inverse of a Matrix

4, 6, 9, 10, 12, 14, 18, 32, 34

2.3

Invertible Matrices

2, 4, 6, 8, 10, 13, 14

2.4

Partitioned Matrices

17, 8, 10

2.5

Matrix Factorizations

1, 5, 7, 9, 13

3.1

Determinants

4, 8, 10, 14, 38

3.2

Properties of Determinants

12, 14, 16, 18, 20, 22, 26, 27, 28

3.3

Cramer's Rule

1, 3, 5, 7, 11, 13, 19, 21, 23, 27, 29, 30, 31

4.1

Vector Spaces and Subspaces

111 odd, 16, 18, 22, 28

4.2

Null Spaces, Column Spaces and Linear Transformations

4, 6, 917 odd, 22, 24, 34

4.3

Linearly Independent Sets; Bases

115 odd, 21, 22, 24, 30

4.4

Coordinate Systems

39 odd, 1416, 20, 28

4.5

Dimension of a Vector Space

513 odd, 22, 29, 30

4.6

Rank

121 odd

4.7

Change of Basis

15, 7, 19

5.1

Eigenvectors and Eigenvalues

915 odd, 26, 32

5.2

Characteristic Equation

2, 6, 10, 14, 16, 18

5.3

Diagonalization

113 odd, 20, 24, 26

5.4

Eigenvectors and Linear Transformations

115 odd

6.1

Inner Product, Length and Orthogonality

19 odd, 11, 17, 23

6.2

Orthogonal Sets

1, 3, 5, 9, 13, 17, 19

6.3

Orthogonal Projections

1, 3, 5, 7

Final Examination
 Friday, December 14, 2:00 p.m.4:00 p.m.

