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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 If it is outdated, click here to do a search.
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