# Matrices resources

### Quick Reference (18)

Addition, subtraction and scalar multiplication of matrices

Matrices 3: This leaflet explains the conditions under which it is possible to add or subtract two matrices. It explains how to perform addition and subtraction when this is possible. It also explains how a matrix can be multiplied by a number. There is an accompanying video tutorial.

Cramer's rule

Cramer's rule can be used to solve simultaneous equations using determinants.
This leaflet states and illustrates the rule. (Engineering Maths First Aid Kit 5.2)

Determinants

This leaflet explains what is meant by a determinant and shows how it can be
evaluated. (Engineering Maths First Aid Kit 5.1)

Eigenvalues and eigenvectors

This leaflet introduces eigenvalues and eigenvectors of a 2x2 matrix. It is contributed to the mathcentre Community Project by Tony Croft and reviewed by Leslie Fletcher.

Example of finding the determinant of a 3x3 matrix

Matrices 10: This leaflet provides an example of calculating the determinant of a 3x3 matrix. There is an accompanying video tutorial.

Matrices - solving two simultaneous equations

Matrices 8: This leaflet explains how matrices can be used to solve a pair of simultaneous equations. There is an accompanying video tutorial.

Matrices - what is a matrix ?

Matrices 1: This leaflet explains what is meant by a matrix, explains the notation used to describe matrices, and introduces some special types of matrix. There is an accompanying video tutorial.

Matrix inversion of a 3x3 matrix

Matrices 11: This leaflet explains how to calculate the inverse of a 3x3 matrix. There is an accompanying video tutorial.

Multiplying matrices

This leaflet explains how to multiply two matrices together. (Engineering Maths First Aid Kit 5.3)

Multiplying matrices 1

Matrices 5: This leaflet introduces the conditions under which matrices can be multiplied. It shows how matrix multiplication is carried out whenever this is possible. There is an accompanying video tutorial.

Multiplying matrices 2

Matrices 6: This leaflet continues to explore the conditions under which matrices can be multiplied. It shows how matrix multiplication is carried out whenever this is possible. There is an accompanying video tutorial.

Symmetric matrices and the transpose of a matrix

Matrices 2: This leaflet explains what is meant by a symmetric matrix and the transpose of a matrix. There is an accompanying video tutorial.

The determinant of a 2x2 matrix

Matrices 4: This leaflet explains what is meant by the determinant of a 2x2 matrix. It explains the terms singular matrix and non-singular matrix. There is an accompanying video tutorial.

The determinant of a 3x3 matrix

Matrices 9: This leaflet explains how to calculate the determinant of a 3x3 matrix. There is an accompanying video tutorial.

The inverse of a 2x2 matrix

This leaflet explains what is meant by the inverse of a 2x2 matrix and how this can be found using a formula. (Engineering Maths First Aid Kit 5.4)

The inverse of a 2x2 matrix

Matrices 7: This leaflet explains what is meant by the inverse of a 2x2 matrix and shows how to calculate this when it exists. There is an accompanying video tutorial.

The inverse of a matrix

This leaflet explains what is meant by the inverse of a matrix and how this can be calculated. (Engineering Maths First Aid Kit 5.5)

Using the inverse matrix to solve equations

This leaflet explains how simultaneous linear equations can be solved by calculating the inverse of an appropriate matrix. (Engineering Maths First Aid Kit 5.6)

### Test Yourself (8)

Determinants Test 01 (DEWIS)

Three questions on finding the determinant of a 2X2 and a 3X3 matrix and finding values of x such that the determinant of a 2X2 is zero. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.

Eigenvalues and eigenvectors Test 01 (DEWIS)

Four questions on finding eigenvalues (both real and complex) of a 2X2 matrix and eigenvectors of a 2X2 and 3X3 matrix. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.

Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

Matrices Test 01 (DEWIS)

Five questions on matrix arithmetic testing matrix addition, scalar multiplication, transpose of a matrix and matrix multiplication. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.

Matrix arithmetic - Numbas

Three questions on linear combinations and products of matrices. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Solving simultaneous equations using matrices - Numbas

1 question. Solve a pair of linear equations in two unknowns by writing an equivalent matrix equation. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Systems of linear equations - Numbas

3 questions. First, two equations in two unknowns; second 3 equations in 3 unknowns, solved by Gauss elimination. The third, two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

### Video (11)

Addition, subtraction and scalar multiplication of matrices

Matrices 3: This video tutorial explains the conditions under which it is possible to add or subtract two matrices. It explains how to perform addition and subtraction when this is possible. It also explains how a matrix can be multiplied by a number. There is an accompanying help leaflet.

Example of finding the determinant of a 3x3 matrix

Matrices 10: This video tutorial provides an example of calculating the determinant of a 3x3 matrix. There is an accompanying help leaflet.

Matrices - solving two simultaneous equations

Matrices 8: This video tutorial explains how matrices can be used to solve a pair of simultaneous equations. There is an accompanying help leaflet.

Matrices - what is a matrix ?

Matrices 1: This video tutorial explains what is meant by a matrix, explains the notation used to describe matrices, and introduces some special types of matrix. There is an accompanying help leaflet.

Matrix inversion of a 3x3 matrix

Matrices 11: This video tutorial explains how to calculate the inverse of a 3x3 matrix. There is an accompanying help leaflet.

Multiplying matrices 1

Matrices 5: This video tutorial introduces the conditions under which matrices can be multiplied. It shows how matrix multiplication is carried out whenever this is possible. There is an accompanying help leaflet.

Multiplying matrices 2

Matrices 6: This video tutorial continues to explore the conditions under which matrices can be multiplied. It shows how matrix multiplication is carried out whenever this is possible. There is an accompanying help leaflet.

Symmetric matrices and the transpose of a matrix

Matrices 2: This video tutorial explains what is meant by a symmetric matrix and the transpose of a matrix. There is an accompanying help leaflet.

The determinant of a 2x2 matrix

Matrices 4: This video tutorial explains what is meant by the determinant of a 2x2 matrix. It explains the terms singular matrix and non-singular matrix. There is an accompanying help leaflet.

The determinant of a 3x3 matrix

Matrices 9: This video tutorial explains how to calculate the determinant of a 3x3 matrix. There is an accompanying help leaflet.

The inverse of a 2x2 matrix

Matrices 7: This video tutorial explains what is meant by the inverse of a 2x2 matrix and shows how to calculate this when it exists. There is an accompanying help leaflet.