IBMaths: AI HLDPRevision Notes1. Number & Algebra1.7 Matrices1.7.1 Introduction to Matrices

Introduction to Matrices (DP IB Maths: AI HL)

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Naomi C

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Naomi C

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Introduction to Matrices

Matrices are a useful way to represent and manipulate data in order to model situations. The elements in a matrix can represent data, equations or systems and have many real-life applications.

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

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What type of matrices are there?

  • A column matrix (or column vector) is a matrix with a single column, n equals 1
  • A row matrix is a matrix with a single row, m equals 1
  • A square matrix is one in which the number of rows is equal to the number of columns, m equals n
  • Two matrices are equal when they are of the same order and their corresponding elements are equal, i.e. 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

Exam Tip

  • 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.

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

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Naomi C

Author: Naomi C

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.