Introduction to Matrices (Edexcel IGCSE Maths B): Revision Note

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"

  • E.g. a 2 × 1 matrix is 

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

    • this could be used to represent the point with coordinates

  • a 2 × 2 matrix is

    • this is called a square matrix (same number of rows and columns)

  • a 2 × 3 matrix is

    • this could be used to represent the vertices of a triangle with coordinates , and

  • a 3 × 3 matrix is

    • this is also a square matrix (same number of rows and columns)

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

  •  ,  

The identity and null matrices

What is the identity (or unit) matrix?

• The identity matrix, , is a square matrix with 1s along the diagonal from top-left to bottom-right and zeros everywhere else

  • The 2×2 identity matrix is

  • The 3×3 identity matrix is

• It is also sometimes known as the unit matrix

  • For matrices, it fulfils a role similar to the number 1 for regular numbers

What is the null (or zero) matrix?

• The null matrix is a matrix with all its elements equal to zero

  • The 2×2 null matrix is

  • The 3×3 null matrix is

• Unlike the identity matrix, the null matrix does not have to be square

  • E.g., the 2×3 null matrix is

• It is also sometimes known as the zero matrix

  • For matrices, it fulfils a role similar to the number 0 (zero) for regular numbers

  • You may sometimes see a bold zero, , used to represent the null matrix