Introduction to Linear Algebra

Traditionally linear algebra was a subject for Mathematics, Engineering and Science majors. However, it has become more popular due to data science and machine learning development. This course introduces you to linear algebra. It explains and demonstrates how to solve systems of linear equations, determine if a transformation is linear and find the eigenvalues and eigenvectors of a matrix. Enhance your skills and learn linear algebra for free!

What You Will Learn In This Free Course

Matrix Arithmetic

This module will teach you what matrices and vectors are and how to perform arithmetic with them. You will also learn what the transpose of a matrix is as well as the dot product of vectors.

Systems of Linear Equations

In this module, you will learn to solve systems of linear equations and be able to determine when a solution exists or does not. You will also learn to produce the row echelon form (REF) and reduced row echelon form (RREF) of a matrix.

Determinants

In this module, you will learn how to calculate the determinant of square matrices. In addition, you will study the relationship between the determinant of a matrix and the invertibility of the matrix. Finally, gain knowledge of the different properties of determinants.

Vector Spaces

In this module, you are introduced to one of the most important topics in linear algebra, which is vector space. In addition, you will gain an understanding of the definitions of vector space, subspace, and linear combinations of vectors.

First Course Assessment

In this module you are tested over the following module contents: Matrix Arithmetic, Systems of Linear Equations, the Matrix Inverse, Determinants, and Vector Spaces.; Module

Linear Transformations

In this module, you will learn how linear transformations operate in linear algebra. We will also study the type of conditions it requires for a transformation to be linear. In addition, we will analyze coordinate systems and find a change of basis.

Orthogonality and Least Squares

In this module, you will learn what it means for vectors to be orthogonal. Grasp how the method of least squares can be used to find “solutions” to systems of equations that are inconsistent.; Module

Eigenvalues and Eigenvectors

In this module, you will learn how to calculate the eigenvalues and eigenvectors of a square matrix, the trace of a square matrix is, and what similar matrices are. You also consider how the trace and the determinant of a matrix relate to the eigenvalues of the matrix.

Second Course Assessment

In this module you will be assessed on the following topics: linear transformations, orthogonality and least squares, and eigenvalues and eigenvectors.; Module

Course assessment