You must have come across the concept of matrices in your secondary classes. It is a very interesting concept that we can use to obtain various solutions in an effective and efficient manner. In a layman’s language, matrices can be defined as the arrangement of various numbers in rows and columns. Their numbers when arranged in rows and columns are known as elements. Matrices are the plural of the matrix. There are various types of matrices like square matrix, rectangular matrix, row matrix, column matrix, null matrix, diagonal matrix, identity matrix, and so on. Various matrices have different properties.
History of Matrices
Till 1880s, we described matrices as an array of numbers. The nine chapters of mathematical art is a book written during the 10th- 2nd Century BC in China. In this book, the Chinese author used an array of numbers to solve simultaneous equations. During 1540s, a famous mathematician called Gerolamo Cardano introduced these concepts along with the concepts of determinants in his famous book, Ars Magna which was published in Europe and became popular there. Seki was a Japanese mathematician who also solved simultaneous equations using the method of arrays in 1683. Between 1700 and 1710, breakthrough development took place in the field of matrices. Sir Gottfried Wilhelm Leibniz encouraged the use of these concepts for finding out various solutions and recording down important information. The mathematician experimented with more than 50 different array systems and finally presented the Crammer’s rule in 1750. During the course of 250 years, this rule still remains one of the most important concepts that we can see in the chapter of matrices. In 1850, the term ‘matrix’ finally came into the picture when James Joseph Sylvester coined it. He made several developments and introduced minors in the subject. He also found out that arithmetic operations like multiplication, subtraction and addition can be carried out in matrices and they are different types.
Applications of Matrices
Matrices have a variety of applications:
- Matrices are widely used in the field of demography, sociology, political science, and so on as it is used to represent important data like infant mortality rate, world population, and so on.
- When it comes to plotting out various surveys, matrices are one of the most effective tools that can be used.
- Along with plotting graphs and dealing with statistics, matrices are used extensively for the purposes of various scientific research and scientific studies.
Inverse of a Matrix
When the arithmetic operation of multiplication is carried out with the inverse of a matrix and a given matrix, the result comes out to be the identity matrix. If we need to find out the inverse of a matrix, it is imperative that we deal with a determinant whose value is not equal to zero. Now, a question will pop into your head. What do you mean by determinants and why do we need to learn about it? Basically, determinants are unique numbers that can be obtained using matrices. Determinants are very useful as they help us obtain the inverse of a matrix. We need the concept of the inverse of a matrix as we cannot carry out the arithmetic operation of division on matrices. Let us now discuss how matrices evolved over the course of time.
Matrices are very fascinating as well as easy concepts to understand. If you want to learn more about the matrices, determinants, and their different properties and types in detail and in a fun and interesting manner, visit Cuemath to book a free session.