Math& 204 ~ Elementary Linear Algebra  
 
 
 

Course Description
An introductory course including systems of linear equations; matrices; the vector space Rn; determinants, Cramer's Rule; applications.

Pre-requisite
Math 151 with a grade of C or higher.

Mode of Delivery (Modes)
Lecture

Offered
Winter

Required for:


Course Content

Text: Linear Algebra and its Applications 4th Ed., Lay, Pearson Publishing

1. Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering

2. Matrix Algebra

2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input—Output Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank

3. Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer’s Rule, Volume, and Linear Transformations

4. Vector Spaces
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains

5. Eigenvalues and Eigenvectors

5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems

6. Orthogonality and Least Squares
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram—Schmidt Process