# MTH 261A : Introduction to Linear Algebra

## Transcript title

Introduction to Linear Algebra

## Credits

2

## Grade mode

Standard letter grades

## Contact hours total

20

## Lecture hours

20

## Recommended preparation

## 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.

## 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.

## Grading methods

Grades will be determined by homework, labs, and midterm and final exams.