Linear equation & Matrices

Linear equation is an equations are equations between two variables that make a straight line when it is graphed. There are many different kind of linear equations, one of them is Matrix (Matrices for plural). Matrices are a set of numbers and expressions arranged in rows and columns and are enclosed with square brackets. They can be added, subtracted and multiplied. Matrices can be used to in many different fields of work such as Engineering and even Business. They can be used to show the number of staff and employees in that work place or what two different branches are selling and how each of them are doing in terms of sales.

Matrices are commonly used when we have to deal with several variables at the same time. They can also be used in our daily life when we need to calculate the battery power outputs and the conversion of energy. Matrices have a long history before reaching the point that it reached in this day and age and enabled us to use it in our daily life and work. Matrices were first introduced during the 2nd century BC but it was never truly been developed until the 17th century when more research was made regarding the subject.

People such as the Babylonians and the Chinese started to research Matrices when their initial research has led them to a simultaneous linear equation which couldn’t be solved only Matrix method. However, The Chinese has reached a higher understanding of Matrices than the Babylonians since the first ever example of Matrices was introduced in the “Nine Chapters on the Mathematical Art” which was written during the Han Dynasty era. During the 1545, a man named Girolamo Cardano who was an Italian doctor and mathematician invented a rule to decode a system of two linear equations which he called “regula da modo”.

This rule made Gabriel Cramer start his research to solve a 2×2 Matrix system, although he did not reach the final step of finding a determinant, his research does lead us to believe that he was taking the correct steps to solve Matrices. The idea of the determinant was first established in Japan during the year 1683, a mathematician by the name Takakazu Seki discovered a method to solve matrices with a determinant but was never shared or worked on until 1730 by a man named Leibniz which furthered the research about determinants and used Carmer’s conclusions in his research.

The determinant reached its modern sense by a man called Augustin Louis Cauchy during 1812, he analyzed the earlier proven theories and add some of his own to finally prove the multiplication theory for Matrices using determinants but his research wasn’t of high level and just focused on their specific work.

The term “Matrix” was first introduced during 1850 by James Joseph Sylvester while he did major changes to the Matrix theory, a few colleague of his called Cayley had interest and eventually introducted the inverse of a matrix. Several other mathematicians realized the potency of Matrices and continued the research but it wasn’t until the 19’s when the Matrix theorem played a major role in today’s education and became one of the most important mathematics topic.

Reference for Matrices & determinants
1) http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Matrices_and_determinants.html
2) http://www-groups.dcs.st-and.ac.uk/history/Biographies/Cauchy.html
3) http://www-groups.dcs.st-and.ac.uk/history/Biographies/Leibniz.html
4) http://www-groups.dcs.st-and.ac.uk/history/Biographies/Seki.html
5) http://www-groups.dcs.st-and.ac.uk/history/Biographies/Cramer.html