Math 316U - Fall Semester 2003 - Lectures

Questions regarding the lectures below can be sent to Prof. Williams by e-mail.

These notes will form the basis for part of the lectures. The remainder of each lecture period will be devoted to answering students' questions and solving problems.

• Lecture 1 (8/27/03) - Introduction to Systems of Linear Equations

• Lecture 2 (8/29/03) - Geometric Interpretations and Review of Vectors

• Lecture 3 (9/1/03) - Matrices and Gauss-Jordan Elimination

• Lecture 4 (9/3/03) - Reduced Row-Echelon Form and Solutions to Systems of Equations

• Lecture 5 (9/8/03) - Matrix-Matrix Multiplication

• Lecture 6 (9/12/03) - Linear Combinations, Linear Independence, and Span

• Lecture 7 (9/15/03) - Basis, Dimension, and Coordinates

• Lecture 8 (9/26/03) - Linear Transformations

• Lecture 9 (10/3/03) - Inverse of a Linear Transformation

• Lecture 10 (10/15/03) - Image and Kernel of a Linear Transformation

• Lecture 11 (10/17/03) - Basis of the Image and Kernel of a Linear Transformation

• Lecture 12 (10/22/03) - Change of Basis of a Linear Transformation

• Lecture 13 (11/3/03) - Determinants

• Lecture 14 (11/5/03) - Properties of the Determinant

• Lecture 15 (11/7/03) - Cramer's Rule

• Lecture 16 (11/12/03) - Eigenvalues and Eigenvectors

• Lecture 17 (11/14/03) - Eigenbasis

• Lecture 18 (11/17/03) - Diagonalization and Powers of a Matrix

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