This course is an introduction to linear algebra. Topics we will cover include basic properties of systems of linear equations, matrices and matrix algebra, determinants, vector spaces, subspaces, linear independence of vectors, basis and dimension of subspaces, linear transformations, eigenvalues and eigenvectors of a matrix, orthogonality of vectors, inner product and length of vectors.

## Coordinate systems for general vector spaces – Part I- MATH 2130

Coordinate vectors, Coordinate Mapping for general vector spaces. Part I

## Linear (in)dependence and Bases for general vector spaces – MATH 2130

Linear (in)dependence and Bases for general vector spaces

## kernel and Range of linear transformations – MATH 2130

Kernel and Range of linear transformations

## (Updated) Abstract vector spaces – MATH 2130

Abstract definition of vector spaces, subspaces, linear (in)dependence and examples

## Cramer’s rule, areas and volumes – MATH 2130

Cramer’s Rule, formula for inverse of a matrix and the geometric description of determinants

## Useful properties of determinants – MATH 2130

Some properties of determinants that can useful for computations

## The Standard Matrix of a Linear Transformation – MATH 2130

The standard Matrix of a Linear Transformation

## Introduction to Linear Transformations – MATH 2130

Introduction to Linear Transformations

## Solution sets of matrix equations – MATH 2130

Describing solution sets in the parametric vector form

## The Matrix Equation AX=B – MATH 2130

A new way to see linear systems: matrices acting on vectors.

## Describing Solutions of a Linear System – MATH 2130

Describing solutions of a Linear System in the parametric way.

## The Row Reduction Algorithm – MATH 2130

The Algorithm to obtain the reduced echelon form of a matrix. Useful to solve linear systems.

## Could there be a linear system with exactly two solutions?

Proof that if a linear system has two distinct solutions, then it has infinitely many solutions.

## Solving Linear Systems – Part I – MATH 2130

Defining the basic rules to solve linear systems

## First definitions – MATH 2130

Presentation covering the basic definitions of the course.