Matrices

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ASFM – Core – Introduction to Matrices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6A Slides (Courtesy of Owen134866)

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths Only for 6F Sections

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• Dr Frost Slides 1-14

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 679a: Add or subtract two matrices.
• 679b: Calculate a scalar multiple of a matrix.
• 679c: Substitute the values of matrices into a simple algebraic expression involving addition, subtraction and scalar multiplication.
• 681a: Determine the transpose of a matrix. (not yet active)
• 679: Exam Practice: Adding and subtracting matrices and scalar multiplication
• 681: Exam Practice: Transpose of a matrix

Videos & Other Multimedia

Multiplying a Matrix by a Scalar – Corbettmaths

Corbett Maths Multiplying a Matrix by a Scalar

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms

• Bossmaths
  • Introduction to Matrices
  • Adding and Subtracting Matrices
• Khan Academy
  • Intro to matrices: Videos & practice
  • Adding & subtracting matrices: Videos & practice

Worksheets

• Dr Austin Maths
  • Introduction to Practice Strips (Word | PDF | Answers)
• MadAsMaths (T. Madas)
  • Matrices Exam Questions Part A Q1, 3 (difficulty 2 of 5)
  • Matrices Practice Matrix Introduction Q1, 2

ASFM – Core – Matrix Multiplication

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6B Slides (Courtesy of Owen134866)

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths Only for 6F Sections

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• Dr Frost Slides 15-19

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 680a: Determine the direct product of a 2×2 and 2×1 matrix. (not yet active)
• 680b: Determine the direct product of a 2×2 and 2×2 matrix. (not yet active)
• 680c: Substitute matrices into a simple matrix algebraic expression involving a single product (up to 2×2). (not yet active)
• 680d: Determine whether two matrices can be multiplied together (are comformable).
• 680e: Determine the direct product of matrices with size 2×2 and 3×2 or 2×3
• 680f: Determine the direct product of matrices with size 3×3 and 3×2 or 2×3 (not yet active)
• 680g: Determine the direct product of a 3×3 and 3×3 matrix. (not yet active)
• 680h: Understand the zero matrix/null matrix, infer its size when used in a matrix expression, and simplify a matrix expression using it. (not yet active)
• 680i: Understand that matrix multiplication is associative but not commutative. (not yet active)
• 680j: Determine the product of a 2×2 and 2×2 matrix involving algebraic elements.
• 680k: Square a matrix. (not yet active)
• 680l: Cube a matrix. (not yet active)
• 680m: Substitute the values of matrices into an algebraic expression involving addition, subtraction, multiplication and scalar multiplication. (not yet active)
• 680n: Determine an unknown value in a matrix given its product with another matrix. (not yet active)
• 680o: Determine two unknown values in a matrix multiplication. (not yet active)
• 680p: Solve a matrix equation given in the form ktextbfX = textbfBtextbfC (not yet active)
• 680q: Determine unknown values in a matrix multiplication where commutativity is achieved. (not yet active)
• 680r: Solve problems where the product of two matrices is the identity matrix textbfI (not yet active)
• 680s: Find constants such that textbfA² can be written in the form atextbfA + btextbfI (not yet active)
• 680: Exam Practice: Multiplying matrices

Other Videos & Multimedia

Multiplying Matrices 2×2 by 2×1 – Corbettmaths

Corbett Maths Multiplying Matrices 2×2 by 2×1

Multiplying Matrices 2×2 by 2×2 – Corbettmaths

Corbett Maths Multiplying Matrices 2×2 by 2×2

Identity Matrix – Corbettmaths

Corbett Maths Multiplying Matrices 2×2 by 2×1

Enrichment Video

Matrix multiplication as composition | Chapter 4, Essence of linear algebra

3Blue1Brown: Matrix multiplication as composition

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths Multiplying Matrices

Worksheets

• Dr Austin Maths
  • Fill in the Blanks (Word | PDF | Answers)
  • Practice Strips (Word | PDF | Answers)
  • Crack the Code (Word | PDF | Answers)
• Corbettmaths
  • Matrices AQA Level 2 Practice Questions & Solutions
• Kuta Software
  • Matrix Multiplication Worksheet
• MadAsMaths (T. Madas)
  • Matrices Exam Questions Part A Q6, 14, 19 (difficulty 2 of 5)
  • Matrices Exam Questions Part B Q48, 57 (difficulty 3 of 5)
  • Matrices Practice Matrix Introduction Q3, 4

ASFM – Core – Determinants of Matrices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Tutorial Videos

A-Level Further Maths: C5-01 Determinant: Introducing Determinants

A-Level Further Maths: C5-01 Determinant: Introducing Determinants by TLMaths

Determinant of 3×3 Matrices, 2×2 Matrix, Precalculus Video Tutorial

Determinant of 3×3 Matrices, 2×2 Matrix, Precalculus Video Tutorial by The Organic Chemistry Tutor

Matrices 4 • Determinants of 2×2 Matrices • CP1 Ex6C • 🎯

Matrices 4 • Determinants of 2×2 Matrices • CP1 Ex6C • 🎯 by Bicen Maths

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6C Slides (Courtesy of Owen134866)

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths Only for 6F Sections

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• Dr Frost Slides 20-26

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 682a: Calculate the determinant of a 2×2 matrix with numeric terms.
• 682b: Calculate the determinant of a 2×2 matrix containing algebraic elements. (not yet active)
• 682c: Determine a constant in a 2×2 matrix given its determinant. (not yet active)
• 682d: Determine whether a 2×2 matrix has an inverse. (not yet active)
• 682e: Determine a constant for which a 2×2 matrix is singular.
• 682f: Determine the values for a constant for which a 2×2 matrix is singular (resulting in a quadratic). (not yet active)
• 682g: Use the property det(AB) = det(A)det(B) to solve matrix problems. (not yet active)
• 683a: Calculate the determinant of a 3×3 matrix with numeric terms.
• 683b: Calculate the determinant of a 3×3 matrix containing algebraic terms. (not yet active)
• 683c: Determine a constant in a 3×3 matrix given its determinant. (not yet active)
• 683d: Determine whether a 3×3 matrix has an inverse. (not yet active)
• 683e: Determine a constant for which a 3×3 matrix is singular.
• 683f: Determine the values for a constant for which a 3×3 matrix is singular (resulting in a quadratic). (not yet active)
• 683g: Factorise the determinant of a 3×3 matrix using row and column operations. (not yet active)
• 682: Exam Practice: Calculating determinants of 2×2 matrices
• 683: Exam Practice: Calculating determinants of 3×3 matrices

Enrichment Video

The determinant | Chapter 6, Essence of linear algebra

3Blue1Brown: The determinant

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths
  • Determinants of 2 × 2 Matrices
  • Determinants of 3 × 3 Matrices

ASFM – Core – Inverse of 2×2 Matrices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Tutorial Videos

A-Level Further Maths: C6-02 Inverse Matrices: Deriving the 2×2 Inverse Matrix

A-Level Further Maths: C6-02 Inverse Matrices: Deriving the 2×2 Inverse Matrix by TLMaths

Inverse of a 2×2 Matrix

Inverse of a 2×2 Matrix by The Organic Chemistry Tutor

Solving Matrix Equations

Solving Matrix Equations by The Organic Chemistry Tutor

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6D Slides (Courtesy of Owen134866)

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths Only for 6F Sections

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• Dr Frost Slides 27-31

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 684a: Calculate the inverse of a 2×2 matrix with numeric terms.
• 684b: Calculate the inverse of a 2×2 containing algebraic terms. (not yet active)
• 684c: Solve a matrix equation given in the form textbfAtextbfX = textbfB
• 684d: Solve a matrix equation given in the form textbfAtextbfX = textbfBtextbfC or textbfAtextbfX = textbfB – textbfC (not yet active)
• 684e: Use a self-inverse property of a matrix to determine unknown values.
• 684f: Determine the product of a matrix inverse and a matrix transpose. (not yet active)
• 684g: Calculate textbfA^-1 textbfB^-1 without finding the inverse of either textbfA or textbfB (not yet active)
• 684: Exam Practice: Inverse of a 2×2 matrix

Enrichment Video

Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra

3Blue1Brown: Inverse matrices, column space and null space

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths Inverses of 2 × 2 Matrices

Worksheet & Activities

• MEI activities from old FP1

ASFM – Core – Inverse of 3×3 Matrices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Tutorial Videos

A-Level Further Maths: C6-10 Inverse Matrices: Finding the Inverse of a 3×3 Matrix

A-Level Further Maths: C6-10 Inverse Matrices: Finding the Inverse of a 3×3 Matrix by TLMaths

How to Find the Inverse of 3×3 Matrix (Matrices 8) | A-Level Further Maths

How to Find the Inverse of 3×3 Matrix (Matrices 8) by Jack's Maths

Inverting 3×3 part 1: Calculating matrix of minors and cofactor matrix | Precalculus | Khan Academy

Inverting 3×3 part 1: Calculating matrix of minors and cofactor matrix by Khan Academy

Inverting 3×3 part 2: Determinant and adjugate of a matrix | Matrices | Precalculus | Khan Academy

Inverting 3×3 part 2: Determinant and adjugate of a matrix by Khan Academy

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6E Slides (Courtesy of Owen134866)

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths Only for 6F Sections

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• Dr Frost Slides 32-38

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 685a: Calculate a minor of an element in a 3×3 matrix.
• 685b: Calculate a cofactor of an element in a 3×3 matrix.
• 685c: Determine the cofactor matrix or adjugate/adjunct matrix. (not yet active)
• 685d: Determine the inverse of a 3×3 matrix with numeric terms only. (not yet active)
• 685e: Determine the inverse of a 3×3 matrix containing algebraic terms. (not yet active)
• 685f: Determine values for which a 3×3 matrix is singular involving trigonometric elements. (not yet active)
• 685g: Solve an matrix equation involving textbfI, requiring a matrix inverse. (not yet active)
• 686a: Prove a matrix identity involving an inverse matrix. (not yet active)
• 685: Exam Practice: Inverse of a 3×3 matrix
• 686: Exam Practice: Algebraic identities involving matrices (not yet active)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths Inverses of 3 × 3 Matrices

ASFM – Core – Solving Equations with Matrices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6F Part 1 Slides (Courtesy of Owen134866)

Matrices 1 • Systems of Equations • CP1 Ex6F • 🎯

Matrices 2 • Forming a System of Equations • CP1 Ex6F • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 39-41

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 687a: Use a given matrix inverse to solve simultaneous equations/systems of equations in 3 variables. (not yet active)
• 687b: Use a matrix inverse to solve simultaneous equations/systems of equations with 3 variables involving an algebraic constant. (not yet active)
• 687c: Form and solve a set of simultaneous equations/systems of equations with 3 variables from a modelled context, by use of an inverse matrix. (not yet active)
• 688a: Solve 3 simultaneous equations/systems of equations using Gaussian elimination / reducing to row echelon form, where there is a unique solution set. (not yet active)
• 688b: Determine if a matrix is in row echelon form and row reduced echelon form. (not yet active)
• 688c: Solve 3 simultaneous equations/systems of equations using Gaussian elimination / reducing to row echelon form, where there is redundancy, expressing the general solution as equations in terms of the n (not yet active)
• 688d: Solve 3 simultaneous equations/systems of equations using Gaussian elimination / reducing to row echelon form, where there is redundancy, expressing the general solution in vector form. (not yet active)
• 688e: Use Gaussian elimination to determine a coefficient in simultaneous equations/systems of equations that leads to redundancy. (not yet active)
• 688f: Use Gaussian elimination to determine a coefficient in simultaneous equations/systems of equations that leads to inconsistency. (not yet active)
• 689a: Use Cramer’s rule to solve simultaneous equations involving two variables. (not yet active)
• 689b: Use Cramer’s rule to solve simultaneous equations involving three variables. (not yet active)
• 687: Exam Practice: Solving simultaneous equations/systems of equations (up to 3 variables) by use of an inverse matrix
• 688: Exam Practice: Gaussian elimination / row reduction and general solutions to simultaneous equations/systems of equations
• 689: Exam Practice: Cramer’s rule (not yet active)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths Matrices and Simultaneous Equations

ASFM – Core – Intersecting Planes

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6F Part 2 Slides (Courtesy of Owen134866)

Matrices 3 • Geometric Interpretations of Systems of Equations • CP1 Ex6F • 🎯

Matrices 4 • Algebra to show Consistency/Inconsistency • CP1 Ex6F • 🎯

Matrices 5 NO SOUND • Further Geometric Interpretations • CP1 Ex6F • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 42-48

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 690a: Understand the geometric significance of the matrix corresponding to linear simultaneous equations/systems of equations being non-singular. (not yet active)
• 690b: Determine the value of a constant in linear simultaneous equations/systems of equations that leads to no unique solution. (not yet active)
• 690c: For linear simultaneous equations/systems of equations corresponding to a singular matrix, determine whether the equations are consistent. (not yet active)
• 690d: For linear simultaneous equations/systems of equations corresponding to a singular matrix, determine the geometric configuration of the planes they represent. (not yet active)
• 690: Exam Practice: Geometrically interpreting the solution and failure of the solution to three simultaneous linear equations

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Whole Topic Videos

Matrices 6 • Population Modelling • CP1 Ex6 ExamQ • 🎯

Bicen Maths Exam Question

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Advanced Highers Matrices Exam Questions & Answers
• Transum
  • Exam-style questions: Matrices
• Pret Homework (@DrBennison)
  • Matrix Operations (@DrBennison, docx)

Activities

• NRICH (student problems)
  • Vectors & Matrices (Further)
• Andy Lutwyche
  • Fill In The Blanks
  • Careless Casey
  • Multiplying Codebreakers
  • (Missing Values) Codebreaker

Worksheets

• MathedUp
  • Matrices1 – 2×2: Questions · Challenge · Answers
• Jethwa Maths
  • 10 Minute Starters: Matrices
• Physics & Maths Tutor
  • CP1 Ch.6 Matrices: Questions by topic
• Dr Austin Maths
  • Introduction to Odd One Out (Word | PDF | Answers)
  • Introduction to True or False (Word | PDF | Answers)
  • Determinants Match-Up (Word | PDF | Answers)
  • Inverse of a 2×2 Matrix Crack the Code (Word | PDF | Answers)
  • Inverse of a 3×3 Matrix Fill in the Blanks (Word | PDF | Answers)
  • Solving Simultaneous Equations Fill in the Blanks (Word | PDF | Answers)
  • Graphical Representations of Simultaneous Equations Sort It Out (Word | PDF | Answers)
  • Matrix Multiplication Fill in the Blanks (Word | PDF | Answers)
  • Matrix Multiplication Crack the Code (Word | PDF | Answers)
  • Using the Identity Matrix Practice Strips (Word | PDF | Answers)