Matrices have long been used to solve linear equations, but they were referred regarded as arrays until the 1800s. The Nine Chapters on the Mathematical Art, published in China between the 10th and 2nd centuries BCE, is the first example of the use of array methods to solve simultaneous equations, including the idea of determinants. With the publication of Ars Magna in 1545, Italian mathematician Gerolamo Cardano introduced the method to Europe. In 1683, the Japanese mathematician Seki solved simultaneous equations using the same array methods. In his work Elements of Curves, published in 1659, Dutch mathematician Jan de Witt used arrays to depict transformations (1659). Between 1700 and 1710, Gottfried Wilhelm Leibniz popularized the use of arrays for recording data or solutions, and he experimented with over 50 different types of arrays in various systems In 1750, Cramer introduced his rule.
The term “matrix” (Latin word which means “womb,” derived from mater—mother) was coined by James Joseph Sylvester in 1850, who saw a matrix as an object that gives rise to a number of determinants now known as minors, that is, determinants of smaller matrices that derive from the original one by removing columns and rows. Sylvester explains in his 1851 paper:
A “Matrix” is a rectangular array of terms from which distinct systems of determinants can emerge, as though from a single parent’s womb.
The Matrices are the arrangements of variables, numbers symbols, or expressions in a rectangular table with varied numbers of columns and rows. The elements of the matrix are the numbers or entries that make up the matrix. The horizontal entries of matrices are referred to as rows, whereas the vertical entries are referred to as columns.
There are several restrictions to follow when executing these matrix operations, such as they can only be added or subtracted if they have the same number of rows and columns, and they can only be multiplied if the first and second columns and rows are identical. Let’s take a closer look at the many sorts of matrices and the laws that govern them. The number of rows and columns in a matrix determines the size of the matrix (also known as the order of the matrix).
By performing operations on matrices such as addition, subtraction, multiplication, and so on, we can solve them. The number of rows and columns determines how matrices are calculated. The number of rows and columns must be the same for addition and subtraction, while the number of columns in the first and second matrices must be equal for multiplication.
The following are the basic operations that can be performed on matrices:
- Matrices addition
- Matrices Subtraction
- Multiplication of Scalars
- Matrices Multiplication
- Transpose of Matrices
- Matrices and Their Uses
The Matrices has a wide range of uses in commerce, research, and social science. Matrices are utilized in the following applications:
Optics is a branch of physics which deals with the concept of light.
- Economic Analysis
- Animation and robotics
- Signal processing and wireless communication
- In science, matrices are used as:
In the field of optics, matrices are employed to account for reflection and refraction. Electrical circuits, quantum mechanics, and resistor conversion of electrical energy all benefit from matrices. In electric circuits, matrices are utilized to solve AC network equations.
Matrices in Mathematical Applications
The use of matrices in mathematics is from the very past, history of use in the solution of linear equations. The Matrices are extremely valuable objects that are found in a wide range of applications. The use of matrices in mathematics is applicable to a wide range of scientific fields as well as mathematical areas. Engineering mathematics are also used in almost every aspect of our day to day lives.
Matrices are used to find collinear points
Matrices can be used to determine whether or not any three points are collinear. If three points A(a,b), B(c,d), and C(e,f) do not form a triangle, they are collinear, and the triangle’s area should be zero.
Use of Matrices in geology
Matrixes are used in geology to conduct seismic surveys. They are used to create graphs, statistics, calculate and conduct scientific studies and research in a variety of subjects. Matrices are also used to represent real-world statistics such as population, infant mortality rate, and so on. They are the most accurate in the survey of the plotting methods.
In economics, very large matrices are used to solve challenges, such as maximizing the use of assets, whether labour or capital, in product manufacture and managing very vast supply networks.
Use of Matrices in Information Technology
Matrix data structures are also used by many IT organizations to track user information, execute search queries, and administer databases. Many systems in the field of information security are built to deal with matrices. Matrices are employed in the compression of electronic data, such as the storing of biometric data in Mauritius’s new Identity Card.