Mathematics 227

# Mathematics 227 Course Outline

## Text: Linear Algebra, 2nd ed., (updated), Lay - Addison Wesley (ISBN 0-201-347741) Study Guide (ISBN 0-201-64847-4) 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, 19-22, 29, 30
1.2 Row Reduction and Echelon Forms 1, 2, 5, 6, 13, 14, 21-24
1.3 Vector Equations 7-12, 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 1-7, 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 1-11 odd, 16, 18, 22, 28
4.2 Null Spaces, Column Spaces and Linear Transformations 4, 6, 9-17 odd, 22, 24, 34
4.3 Linearly Independent Sets; Bases 1-15 odd, 21, 22, 24, 30
4.4 Coordinate Systems 3-9 odd, 14-16, 20, 28
4.5 Dimension of a Vector Space 5-13 odd, 22, 29, 30
4.6 Rank 1-21 odd
4.7 Change of Basis 1-5, 7, 19
5.1 Eigenvectors and Eigenvalues 9-15 odd, 26, 32
5.2 Characteristic Equation 2, 6, 10, 14, 16, 18
5.3 Diagonalization 1-13 odd, 20, 24, 26
5.4 Eigenvectors and Linear Transformations 1-15 odd
6.1 Inner Product, Length and Orthogonality 1-9 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.