# MTH 261A : Introduction to Linear Algebra

## Transcript title

Introduction to Linear Algebra

## Credits

2

## Grading mode

Standard letter grades

## Total contact hours

20

## Lecture hours

20

## Prerequisites

MTH 112Z or higher (except MTH 211, MTH 212, MTH 213, MTH 244, and STAT 243Z) or minimum placement Math Level 22.

## Course Description

Provides an introduction to linear algebra concepts for science, math, and engineering majors. Topics include vectors, matrices, systematic solution to linear systems, determinants, linear dependence and independence, linear transformations, and eigenvalues and eigenvectors.

## Course learning outcomes

1. Use matrix notation, basic properties of determinants, and algebraic properties of matrices to express and solve linear systems of equations.

2. Apply properties of vector algebra to solve two- and three-dimensional geometric problems.

3. Describe a linear transformation given the corresponding matrix, and find a matrix given the description of the linear transformation.

4. Determine linear dependence and independence for a set of n vectors in n-space.

5. Find the characteristic polynomial and eigenvalues/eigenvectors of particular (small) matrices and explain the concepts as they apply to matrices of any size.

## Content outline

- Vectors
- Vector definitions and computation
- Dot products, projections, and components
- Vector equations of lines and planes
- Cross products

- Matrices
- Solving systems of equation with matrices
- Gauss-Jordan elimination
- Determinants
- Matrix operations
- Matrix inverse
- Transpose

- Relationships between vectors and matrices
- Dependence and independence of vectors
- Matrices as transformations
- Projections
- Eigenvalues and eigenvectors

## Required materials

A textbook is required.