# Further Mathematics - Exam Revision

## Matrices ... What are they?

Authored By Carmen Popescu-Rose 0 Comment(s)

What is a matrix?

A matrix is a useful way of representing linear relationships between variables.

Matrices look like grids or tables with lists of numbers written in rows and columns.

 This matrix has 2 horizontal lists of numbers called rows.

 This matrix has 3 vertical lists of numbers called columns.

Each element appears at the intersection between a row and a column.

 This matrix has 6 elements.

 This element is in row 2 and column 3.

Converting a two-way table into a matrix

The data in the table below shows that, in a group of 50 children, 5 girls have cats as pets, 17 girls have dogs as pets, 3 boys have cats as pets and 25 boys have dogs as pets.

 Pets ... and here is its corresponding matrix Gender 5 17 3 25

Types of matrices

 Row matrices * one row only Column matrices * one column only Square matrices * number of rows = number of columns Identity matrices * 1s on the leading diagonal * 0s elsewhere Diagonal matrices * any numbers on the leading diagonal * 0s elsewhere Zero matrices * all elements are 0s Upper triangular matrices * all elements below the leading diagonal are 0s Lower triangular matrices * all elements above the leading diagonal are 0s