IBMathsDPApplications & Interpretation (AI)HLRevision Notes1. Number & AlgebraMatricesIntroduction to Matrices

Introduction to Matrices (DP IB Applications & Interpretation (AI)): Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

Introduction to matrices

What are matrices?

  • A matrix is a rectangular array of elements (numerical or algebraic) that are arranged in rows and columns

  • The order of a matrix is defined by the number of rows and columns that it has

    • The order of a matrix with m rows and n columns is m cross times n

      • e.g. the matrix open parentheses table row 1 3 row cell negative 2 end cell 0 row 1 2 end table close parentheses has order 3 × 2

  • A matrix bold italic A can be defined by bold italic A equals left parenthesis a subscript i j end subscript right parenthesis where i equals 1 comma space 2 comma space 3 comma space... comma space m and j equals 1 comma space 2 comma space 3 comma space... comma space n

    • a subscript i j end subscript refers to the element in row i and column j

Matrix A, 2 rows by 3 columns, elements a1,1 to a2,3. Notation shows matrix size with n=3 columns and m=2 rows.
Example of a matrix with order 2 × 3

What type of matrices are there?

  • A column matrix (or column vector) is a matrix with a single column, n equals 1

    • e.g. open parentheses table row 1 row 0 row cell negative 2 end cell end table close parentheses

  • A row matrix is a matrix with a single row, m equals 1

    • e.g. open parentheses table row 1 0 cell negative 2 end cell end table close parentheses

  • A square matrix is one in which the number of rows is equal to the number of columns, m equals n

    • e.g. open parentheses table row 1 2 row 0 cell negative 1 end cell end table close parentheses

  • Two matrices are equal when they are of the same order and their corresponding elements are equal

    • bold italic A equals bold italic B if a subscript i j end subscript equals b subscript i j end subscriptfor all elements

  • A zero matrix, bold italic O, is a matrix in which all the elements are 0

    • e.g. bold italic O equals open parentheses table row 0 0 row 0 0 end table close parentheses

  • The identity matrix, bold italic I, is a square matrix in which all elements along the leading diagonal are 1 and the rest are 0

    • e.g. bold italic I equals open parentheses table row 1 0 row 0 1 end table close parentheses

Examiner Tips and Tricks

Make sure that you know how to enter and store a matrix on your GDC.

Worked Example

Let the matrix bold italic A equals open parentheses table row 5 cell negative 3 end cell 7 row cell negative 1 end cell 2 4 end table close parentheses

a) Write down the order of bold italic A.

nIKgir9C_1-7-1-ib-ai-hl-introduction-to-matrices-we-1a-solution

b) State the value of a subscript 2 comma 3 end subscript .

8~aiP3aD_1-7-1-ib-ai-hl-introduction-to-matrices-we-1b-solution

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths Content Creator

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject 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.