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GCSEFurther MathsAQARevision Notes5. Matrix TransformationsMatrix MultiplicationIntroduction to Matrices

Introduction to Matrices (AQA GCSE Further Maths)

Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Introduction to Matrices

What is a matrix?

  • A matrix is a rectangular grid (array) of elements (numbers or letters) arranged in rows and columns

    • They are used a lot in computer / data science

    • The plural of "matrix" is "matrices"

  • The order of a matrix is its "number of rows" × "number of columns"

    • a 2 × 1 matrix is open parentheses table row a row b end table close parentheses

      • this is also called a column matrix or a column vector

    • a 2 × 2 matrix is open parentheses table row a b row c d end table close parentheses

      • this is called a square matrix

  • A bold capital letter is often used to represent a matrix

    •  bold A equals open parentheses table row 5 2 row 0 4 end table close parentheses, bold B equals open parentheses table row 4 row 3 end table close parentheses

  • 2D coordinates can be written in a column matrix

    • The point (3, 5) is open parentheses table row 3 row 5 end table close parentheses 

How do I multiply a matrix by a scalar?

  • To multiply any matrix by a scalar (a number), multiply each element by that scalar 

    • If bold A equals open parentheses table row 5 2 row 0 4 end table close parentheses then 2 bold A equals 2 open parentheses table row 5 2 row 0 4 end table close parentheses equals open parentheses table row cell 2 cross times 5 end cell cell 2 cross times 2 end cell row cell 2 cross times 0 end cell cell 2 cross times 4 end cell end table close parentheses equals open parentheses table row 10 4 row 0 8 end table close parentheses

  • Lower case letters often refer to scalar multiples

    • k bold A is the matrix bold Amultiplied by the scalar k

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    Author
    Reviewer
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.