IGCSEMathsEdexcelMaths BRevision NotesMatricesProperties of MatricesDeterminants of Matrices

Determinants of Matrices (Edexcel IGCSE Maths B): Revision Note

Exam code: 4MB1

Roger B

Written by: Roger B

Reviewed by: Jamie Wood

Updated on

Determinant of a 2x2 matrix

What is a determinant?

  • The determinant is a numerical value (positive or negative) calculated from the elements in a matrix

    • It is used to find the inverse of a matrix

  • You can only find the determinant of a square matrix

  • For a 2 cross times 2 matrix open parentheses table row a b row c d end table close parentheses 

    • The determinant is equal to a d minus b c

Examiner Tips and Tricks

The formula for the determinant is on the course Formulae sheet, and will be provided for you in Paper 2 questions where it is needed.

However, determinant questions can also appear in Paper 1, so be sure you know the formula going into the exam.

  • The notation det is sometimes used to indicate the determinant

    • So det bold A refers to the determinant of matrix bold A

    • E.g. if A equals open parentheses table row 3 4 row cell negative 2 end cell cell negative 1 end cell end table close parentheses

      • then det bold A equals 3 cross times open parentheses negative 1 close parentheses minus 4 cross times open parentheses negative 2 close parentheses equals negative 3 minus open parentheses negative 8 close parentheses equals 5

Worked Example

bold A and bold B are two matrices such that the determinant of bold A is equal to the determinant of bold B.

Given that bold A equals open parentheses table row cell square root of p end cell cell negative 1 end cell row 3 cell negative 7 end cell end table close parentheses and bold B equals open parentheses table row 2 4 row 5 1 end table close parentheses, where space p is a positive integer, find the value of space p.

Answer:

Use det open parentheses table row a b row c d end table close parentheses equals a d minus b c to find the determinants of the two matrices

det bold A equals square root of p cross times open parentheses negative 7 close parentheses minus open parentheses negative 1 close parentheses cross times 3 equals 3 minus 7 square root of p

det bold B equals 2 cross times 1 minus 4 cross times 5 equals negative 18

Set the two determinants equal and solve for space p

table row cell negative 18 end cell equals cell 3 minus 7 square root of p end cell row cell 7 square root of p end cell equals cell 3 plus 18 end cell row cell 7 square root of p end cell equals 21 row cell square root of p end cell equals 3 end table

space p equals 3 squared equals 9

space p equals 9

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    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

    Jamie Wood

    Reviewer: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.