Matrices and Vectors

The resources below revisit complex Maths topics included your STEM course. Watch the videos and work through the exercises to boost your knowledge and understanding. If you need to 'dig deeper', please check the Higher section on the previous page or if you are looking for something more specific, use "Ctrl+F" for a faster search.

Enjoy your learning!

Vectors

Introduction to Vectors

• Video: Intro to vectors & scalars | One-dimensional motion
• Exercise booklet introducing vectors 

Cartesian components of vectors

• Video: The Magnitude / Length of a 2D Vector
• Exercises on Cartesian components of vectors 

Lines and planes

• Video: Introducing the Vector Equation of a Line
• Exercises on Lines and Planes

Scalar product

• Video: Finding the Angle Between Two Points
• Exercises on Scalar Products 

Vector product

• Video: The Vector Cross Product
• Exercises with solutions on vector products

Matrices

Introduction to matrices

• Video: Introducing Matrices
• HELM Booklet on matrices

Addition and subtraction

• Video: Matrix Addition and Subtraction

Multiplication

• Video: Multiplying matrices by scalars
• Video: Matrix Multiplication
• HELM exercises on matrix multiplication

Determinants

• Video: Finding the Determinant of a 2x2 matrix
• HELM Exercise and Solution Booklet on matrix determinants

The inverse of a matrix

• Video: How to work out the inverse of a matrix
• HELM Exercises on Matrix Inverse  

Eigenvectors and eigenvalues - Introduction

• Video: Introduction to Eigenvectors and eigenvalues
• HELM Exercises on Eigenvectors and eigenvalues

Applications of eigenvalues and eigenvectors

• Video: The applications of eigenvectors and eigenvalues
• HELM Exercises on Eigenvectors and eigenvalue applications

Repeated eigenvalues and symmetric matrices

• Video: Symmetric Matrices (Even with Repeated Eigenvalues) Have Orthogonal Eigenvectors
• HELM exercises on eigenvalues and symmetric matrices

Numerical determination of eigenvalues and eigenvectors

• Video: Eigenvalue Power Method (Example): Numerical Methods for Engineers
• HELM exercises on numerical determination of eigenvalues and eigenvectors
• Video: Eigenvalue Power Method

Solving Systems of Equations

Gaussian elimination

• Video: Gaussian elimination: Matrix Algebra for Engineers
• Video Gaussian Elimination and Row Echelon Form
• HELM Exercises Booklet on Gaussian elimination

Solution by Cramer's rule

• Video: Cramer's Rule - 3x3 Linear System (using matrices to solve Sims with 3 unknowns)
• HELM Exercise Booklet on using Cramer's rule to solve sims

Solution by inverse matrix method

• Video: Solving Linear Equations using the Inverse Matrix Method 2x2
• HELM BookletVideo Gaussian Elimination and Row Echelon Form

LU decomposition

• Video: Using lower diagonal and upper diagonal matrix decomposition
• HELM Exercises with worked solutions on LU matrix decomposition

Matrix norms

• Video: Numerical Methods: Vector and Matrix Norms
• HELM Booklet on matrix norms

Iterative methods for systems of equations

• Video: Introduction to Iterative Methods For Linear Systems
• HELM Exercise booklet on successive iterates

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