**Catalog Description:** Systems of linear equations, matrices and
determinants. Vector spaces and linear transformations.

Eigenvalues, eigenvectors, diagonalization of a symmetric matrix.

** Prerequisites :** Math 135 and Math 152 with grade of C or higher.

**Textbook:** Elementary Linear Algebra, 6^{th }edition, by Larson, Edwards, and
Falvo.

**Course Outline and Topics**

Chapter 1: Systems Of Linear Equations

1.1: Introduction to Systems of Linear Equations

1.2: Gaussian Elimination and Gauss -Jordan Elimination

1.3: Applications of Systems of Linear Equations

Chapter 2: Matrices

2.1: Operations with Matrices

2.2: Properties of Matrix Operations

2.3: The Inverse of a Matrix

2.4: Elementary Matrices

Chapter 3: Determinants

3.1: The Determinant of a Matrix

3.2: Evaluation of a Determinant Using Elementary Operations

3.3: Properties of Determinants

3.4: Introduction to Eigenvalues

Chapter 4: Vector Spaces

4.1: Vectors in R^{n}

4.2: Vector Spaces

4.3: Subspaces of Vector Spaces

4.4: Spanning Sets and Linear Independence

4.5: Basis and Dimension

4.6: Rank of a Matrix and Systems of Linear Equations

4.7: Coordinates and Change of Basis

Chapter 5: Inner Product Spaces

5.1: Length and Dot Product in R ^{n}

5.2: Inner Product Spaces

5.3: Orthonormal Bases: Gram-Schmidt Process

Chapter 6: Linear Transformations

6.1: Introduction to Linear Transformations

6.2: The Kernel and Range of a Linear Transformation

6.3: Matrices for Linear Transformations

6.4: Transition Matrices and Similarity

Chapter 7: Eigenvalues And Eigenvectors

7.1: Eigenvalues and Eigenvectors

7.2: Diagonalization

7.3: Symmetric Matrices and Orthogonal Diagonalization