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Unsure about the Inverse of a Matrix?

Unsure about the Inverse of a Matrix?

Let the fantastic wealth of resources below teach you all about the Inverse of a Matrix.

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Covers the whole of the AH Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

Inverse of a Matrix

Welcome to advancedhighermaths.co.uk

A sound understanding of the Inverse of a Matrix is essential to ensure exam success.

Study at Advanced Higher Maths level will provide excellent preparation for your studies when at university. Some universities may require you to gain a pass at AH Maths to be accepted onto the course of your choice. The AH Maths course is fast paced so please do your very best to keep on top of your studies.

For students looking for extra help with the AH Maths course in 2020/21 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.

We hope you find this website useful and wish you the very best with your studies in 2020/21.

Please find below:

1. AH Maths Past Exam Worksheets by Topic

2. Links and Exam Formulae

3. Matrices Resources

4. MIA Text Book Questions – Matrices

5. About the Inverse of a Matrix

6. AH Maths Past & Practice Papers

7. AH Maths Past Paper Questions by Topic

8. AH Maths Recommended Text Book

9. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass

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Advanced Higher Maths Resources

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1. AH Maths Past Paper Exam Worksheets by Topic

Thanks to the SQA for making these available. The worksheets by topic below are an excellent study resource since they are actual SQA past paper exam questions.

Clear, easy to follow, step-by-step worked solutions to all SQA Higher Maths Questions below are available in the Online Study Pack.

Number
______		Topic
____________________________________________		Answers
_________
1Binomial TheoremAnswers
2Complex NumbersAnswers
3DifferentiationAnswers
4Differentiation (Further)Answers
5Differential Equations - Variables SeparableAnswers
6Differential Equations (Further)Answers
7Functions & GraphsAnswers
8IntegrationAnswers
9Integration (Further)Answers
10MatricesAnswers
11Number Theory - Methods of ProofAnswers
12Number Theory (Further) - Euclidean & Number BasesAnswers
13Partial FractionsAnswers
14Sequences & SeriesAnswers
15 Sequences & Series - Maclaurin Answers
16Systems of EquationsAnswers
17VectorsAnswers

2. Links and Exam Formulae

AH Maths - Home Page LinkHERE
AH Maths - Whole Course LinkHERE
AH Maths - Exam Formula ListHERE
Higher Maths - Exam Formulae ListHERE
AH Maths - Complete Formula ListHERE
SQA Full Course Content and OutlineHERE

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3. Matrices Resources

Thanks to the author(s) for making these available.

Matrices Theory Guide 1HERE
Matrices Theory Guide 2HERE
Matrices Theory Guide 3HERE
Matrices HSN Summary NotesHERE

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4. MIA Text Book Questions – Matrices

Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Subtopic
__________________________________		Page Number
_____________		Exercise
______________		Recommended Questions
____________________________
Basic Properties & Operations of MatricesPage 231Exercise 13.1Q1,2,3a,4a,c,e,i,p,t,7a,f,9,10
Matrix MultiplicationPage 235Exercise 13.3Q1a,c,2a,c,k,m,o,3a,4,5a,c
Properties of Matrix MultiplicationPage 236Exercise 13.4Q6a,b,7a,b,8a
Determinant of a 2 x 2 MatrixPage 240Exercise 13.6Q1a,b,d,h
Determinant of a 3 x 3 MatrixPage 247Exercise 13.9Q4a,b,c,d,5a,b
Inverse of a 2 x 2 MatrixPage 243Exercise 13.7Q1,2,4,8,9a,b,c
Inverse of a 3 x 3 MatrixPage 275Exercise 14.10Q1a,b,c,d
Transformation MatricesPage 251Exercise 13.10Q1,2,5

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5. About the Inverse of a Matrix

For a more detailed explanation, please first read the Theory Guides above.

For an inverse of a matrix to exist the matrix must be square and the determinant non-zero.

Inverse of a 2 x 2 Matrix

Inverse of a 3 x 3 Matrix

It can be shown that the same set of elementary row operations which change a square matrix A into the identity matrix I can also change the identity matrix I into the inverse matrix  (if it exists).

This fact can be used to find the inverse of a matrix from scratch.

To read a clear seven step example how to find the inverse of a 3 x 3 matrix please click Theory Guide One and refer to the section titled “The Inverse of a 3 x 3 Matrix” (Pages 22 to 24).

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6. AH Maths Past & Practice Papers

Thanks to the SQA for making these available.

Worked solutions to SQA Exam Questions available in the Online Study Pack.

Year
____		Paper Type
_________________		Exam Paper
______________		Marking Scheme
_______________________________________
2019AH SpecimenSpecimenMarking Scheme
2019Advanced HigherExam PaperMarking Scheme
2018Advanced HigherExam PaperMarking Scheme
2017Advanced HigherExam PaperMarking Scheme
2016Advanced HigherExam PaperMarking Scheme
2016AH SpecimenSpecimenMarking Scheme
2016AH ExemplarExemplarMarking Scheme
2015Advanced HigherExam PaperMarking Scheme
2014Advanced HigherExam PaperMarking Scheme
2013Advanced HigherExam PaperMarking Scheme
2012Advanced HigherExam PaperMarking Scheme
2011Advanced HigherExam PaperMarking Scheme
2010Advanced HigherExam PaperMarking Scheme
2009Advanced HigherExam PaperMarking Scheme
2008Advanced HigherExam PaperMarking Scheme
2007Advanced HigherExam PaperMarking Scheme
2006Advanced HigherExam PaperMarking Scheme
2005Advanced HigherExam PaperMarking Scheme
2004Advanced HigherExam PaperMarking Scheme
2003Advanced HigherExam PaperMarking Scheme
2002Advanced HigherExam PaperMarking Scheme
2001Advanced HigherExam PaperMarking Scheme

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7. AH Maths Past Paper Questions by Topic

Thanks to the SQA for making these available.

Questions and answers have been split up by topic for ease of reference.

Worked solutions to all SQA questions below available in the Online Study Pack.

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Paper
___________		.
Marking
______		Binomial
Theorem
________		Partial
Fractions
________		.
Differentiation
___________		Further Differentiation
___________		.
Integration
___________		Further
Integration
____________		Functions
& Graphs
___________		Systems of
Equations
____________		Complex
Numbers
__________		Seq &
Series
_________		Further Seq
& Series
____________		.
Matrices
_________		.
Vectors
__________		Methods
of Proof
__________		Further No
Theory
___________		Differential
Equations
____________		Further
Differential Eqns
_________________
Specimen P1MarkingQ2Q4Q6Q8Q3Q5Q1Q7
Specimen P2MarkingQ3Q1Q2,4,8,10Q7Q11Q5Q13Q9Q6Q12
2019MarkingQ9Q4Q1a,b,6Q1c,5,10Q16bQ16aQ3Q18Q7,17Q2Q15Q11,14Q12Q13Q8
2018MarkingQ3Q2Q1bQ1a,c,6,13Q8Q15aQ16aQ4,10Q14Q17Q7,11Q16Q9,12Q5Q15b
2017MarkingQ1Q2Q3Q11,18Q16Q6Q12Q5Q17Q4,10Q7Q15Q13Q8Q9Q14
2016MarkingQ3Q13Q1a,bQ1c,11Q13Q9Q12Q4Q8Q2Q6Q7Q14Q5,10Q16Q15
2015MarkingQ1,9Q2Q4,6,8Q17Q10Q14Q13Q3Q5,11Q15Q12Q7Q18Q16
2014MarkingQ214bQ1,13Q1,4,6Q10,12Q15Q11Q3Q16Q14Q9Q7Q5Q7Q8
2013MarkingQ1Q2Q11Q4,6Q8Q13Q7,10Q17Q3Q15Q9,12Q5Q16Q14
2012MarkingQ415aQ1Q12,13Q8Q11Q7Q14Q3,16bQ2Q6Q9Q516aQ10Q15
2011MarkingQ2Q13b,73aQ1,11aQ1,11,16Q6Q10Q8,13Q5Q4Q15Q12Q9Q14
2010MarkingQ5Q1Q13Q15Q3,7Q10Q16Q2Q9Q4,14Q6Q8,12Q11
2009MarkingQ8Q14Q1aQ1b,11Q5,7Q9Q1316aQ6Q12Q14Q2Q16Q4Q10Q3Q15
2008MarkingQ8Q4Q10,15Q2,5Q4,9,10Q7Q3Q16Q1Q12Q6Q14Q11Q13
2007MarkingQ1Q4Q2Q13Q4,10Q4Q16Q3,11Q9Q6Q5Q15Q12Q7Q14Q8
MixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixed

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8. AH Maths Text Book – Maths In Action (2nd Edition) by Edward Mullan 

A fully revised course for the new Curriculum for Excellence examination that is designed to fully support the course’s new structure and unit assessment. A part of the highly regarded Maths in Action series, it provides students with a familiar, clear and carefully structured learning experience that encourages them to build confidence and understanding.

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9. Exam focused Online Study Pack

Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about the Inverse of a Matrix to pass your final exam.

As well as students studying Advanced Higher Mathematics, the resources will benefit young adults studying A-Level Mathematics and undergraduates who need a little extra help. Particular benefit will be to students who have gained a ‘Conditional’ University place and are therefore required to pass in order to gain entry onto the course of their choice.

Subscribing to the Online Study Pack may therefore be one of your best ever investments. Please click Online Study Pack to view screenshots, examples and instructions on how to subscribe.

Please speak with your mum/dad and show them our fantastic website.

We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2020/21.

Get the Study Pack - just £9.99

Teachers click here >

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