GCSEFurther MathsAQARevision Notes5. Matrix TransformationsMatrix MultiplicationIntroduction to Matrices

Introduction to Matrices (AQA GCSE Further Maths)

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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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    Mark

    Author: Mark

    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.