**HISTORY OF MATRICES**

Matrices began in the 2nd century BC with the **Chinese**
although traces could be seen back in the 4th century BC with the Babylonians.
The text *Nine Chapters of the Mathematical Art* written during the
Han Dynasty in China gave the first known example of matrix methods. They
were used to solve simultaneous linear equations.

You have learnt how to solve 2 simultaneous linear equations in 2 unknowns
using the **elimination method** and the
**substitution method**. What about 3 simultaneous
linear equations in 3 unknowns? And 4 simultaneous linear equations in
4 unknowns? The usual methods are very tedious when the number of unknowns
are big. That is why we learn the **matrix method**
which uses the inverse of a matrix. (Fortunately, computers have an efficient
algorithm or method to calculate the inverse of an n x n matrix when n
is big. Otherwise, the matrix method will also be tedious.) You will get
to learn this method for solving 2 simultaneous linear equations later
on.

Please note that the website below describes the ** ancient**
matrix method used to solve 3 simultaneous linear equations. It is different
from the modern approach using the inverse of a matrix.

It was only towards the end of the 17th century that much progress was
made on the studies of matrices. **Carl Gauss**
(1777-1855), the greatest German mathematician of the 19th century, first
used the term 'determinant' in 1801 although its meaning was not exactly
the same. It was **Augustin Cauchy** (1789-1857),
a great French mathematician, who used 'determinant' in 1812 in the modern
sense of the word. **James Sylvester**
(1814-1897), an English mathematician and lawyer, was the first to use
the term 'matrix' in 1850.

But it was his colleague, **Arthur Cayley**
(1821-1895), another English mathematician and lawyer, who first published
an abstract definition of a matrix in his *Memoir on the Theory of Matrices*
in 1858, thus establishing it as a branch of mathematics. Prior to this,
all other mathematicians viewed matrices only in the specific contexts
in which they were working; they failed to generalise the idea of matrices.

You can find out more about matrices from the following site. If it is outdated, click here to do a search.

www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Matrices_and_determinants.html

**[Return to Lesson]**

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