All sections are from "Contemporary Linear Algebra" by Anton and Busby.

Note: You may choose to pre-read for the lectures or post-read. Experiment to find what works for you.

Week Number:

- May 7-8
- Section 1.1 Vectors - addition, multiplication by a scalar, magnitude, applications, n-space, Cartesian co-ordinate systems, algebraic description of vectors, multiplication by a scalar and addition of vectors
- Section 1.2 Dot Product - norms, unit vectors, standard unit vectors, normalization

May 9-10

- Section 1.3 Vector and Parametric Equations of Lines and Planes
- Section 2.1 Introduction to Systems of Linear Equations; Constants and variables; order of operations, solutions, matrices, row operation

- Section 2.2 Solving Linear Systems by Row Reduction, Reading off a solution from a matrix in row-echelon form, Gauss-Jordan elimination;
- Section 2.3 Applications -
Balancing chemical equations, Polynomial interpolation

May 16-17

- Section 3.1 Operations on Matrices - Addition, multiplication by a scalar, transpose, and matrix multiplication
- Section 3.2 Inverses; Algebraic Properties of Matrices
- Section 3.3 Elementary Matrices; a Method for Finding the Inverse of a Matrix.

May 22-23

- Section 3.3 continued - Unifying Theorem (Theorem 3.3.9) Conditions a) - f);
- Section 3.4 Subspaces of R
^{n }, Linear Independence – Examples, -Theorem 3.4.7; Transpose.

May 24 - Mid-term exam in class

- Unifying Theorem (Theorem 7.4.4) Conditions k) and l); Section 1.2 Dot Product and Orthogonality
- Section 3.5 The Geometry of Linear Systems
- Section 4.1 Determinants; Co-factor expansion

May29-30

- Section 4.2 Properties of Determinants
- Section 4.3
Formula for A
^{-1}; Cramer's Rule; Applications

- Section 4.3 continued; Cross-Product, Vandermonde determinants
- Section 4.4 Fixed Points, A First Look at Eigenvalues and Eigenvectors

June 6-7

- Section 4.4 continued,
- Section 6.1 Introduction to Linear Transformations
- Section
6.2 Geometry of Linear Operators - Orthogonal Operators on R
^{2}; start of Section 6.3 Kernel and Range

- Section 6.3 Kernel and Range, continued
- Section 6.4 Composition and Invertibility of Linear Transformations
- Section 7.1 Basis and Dimension

June13

- Section 7.1 continued - linear independence
- Review.

June 14 -Final-exam;

End of Classes.

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