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Matrices ... What are they?
In Further Mathematics - Exam Revision

Matrices ... What are they?

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.

... and here is its corresponding matrix





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


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