#### Description

Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms. All sections of the course will use the software system MATLAB. Credit will be granted for only one of the following: MATH 240 or MATH 341 or MATH 461.

#### Prerequisites

a C- or better in (MATH 131 or MATH141)

**Topics**

**Systems of Linear Equations**

Gaussian elimination

Matrix operations

Finding the inverse

Solution spaces

**Determinants**

Definition

Evaluation

Minors

Cramer's Rule

**Vectors in 2- and 3- space**

Geometric and algebraic definitions

Dot product

Projections

**Vector Spaces**

Euclidean space

Subspaces

Linear independence

Basis and dimension

Row space, rank

Length and angle

Gram-Schmidt

Least squares

**Linear Transformations**

Definition

Kernel and range

Representation as matrices

**Eigenvalues and Eigenvectors**

Definition

Diagonalization

Orthogonal diagonalization

Symmetric matrices

**Applications**

Differential equations

Quadratic forms

Numerical methods