Introduction to Matrices (AQA GCSE Further Maths)

Revision Note

Written by: Mark Curtis

Reviewed by: Dan Finlay

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 $(\begin{matrix} a \\ b \end{matrix})$
  - this is also called a column matrix or a column vector
- a 2 × 2 matrix is $(\begin{matrix} a & b \\ c & d \end{matrix})$
  - this is called a square matrix
A bold capital letter is often used to represent a matrix
- $A = (\begin{matrix} 5 & 2 \\ 0 & 4 \end{matrix})$ , $B = (\begin{matrix} 4 \\ 3 \end{matrix})$
2D coordinates can be written in a column matrix
- The point (3, 5) is $(\begin{matrix} 3 \\ 5 \end{matrix})$

To multiply any matrix by a scalar (a number), multiply each element by that scalar
- If $A = (\begin{matrix} 5 & 2 \\ 0 & 4 \end{matrix})$ then $2 A = 2 (\begin{matrix} 5 & 2 \\ 0 & 4 \end{matrix}) = (\begin{matrix} 2 \times 5 & 2 \times 2 \\ 2 \times 0 & 2 \times 4 \end{matrix}) = (\begin{matrix} 10 & 4 \\ 0 & 8 \end{matrix})$
Lower case letters often refer to scalar multiples
- $k A$ is the matrix $A$ multiplied by the scalar $k$

Last updated: 5 October 2024

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