Matrices are one of the powerful and essential tools in modern Mathematics. This Mathematical tool will simplify our work to a great extent when compared with other direct methods. The evolution of the concept of the matrices is the result of the attempt to get short and simple ways of solving the system of linear equations. Matrices are used not only as a representation of the coefficients in a system of linear equations. The use of the matrices will have many more such applications. These mathematical tools are not only useful in certain branches of the sciences but also in the genetics, economics, sociology, modern psychology as well as in industrial management. This topic is extremely important for both CBSE board exams and competitive exams. Students must practice the concepts and problems of Matrix Formula.
This chapter will strengthen the student’s basic and conceptual fundamentals. This chapter will help the students to understand matrices in an easy and self-explanatory way. The conceptual background of the matrices is also necessary for many other branches of mathematics. Matrices are one of the most useful tools in mathematics as well as other areas of science like cryptography, genetics, economics, sociology, modern psychology and industrial management, etc.
It will simplify our work to a great extent when compared with other straight forward methods. Matrices are not only applicable for the representation of the coefficients in the system of linear equations but also useful the personal computer. Matrices are useful to deal with arranging and organizing them in a proper form of the table. Students will also learn about many ways to apply matrices with determinants. This chapter covers all aspects of matrices with their types, operations, and applications.
A matrix is an ordered rectangular collection of numbers or functions. These numbers are called the elements or the entries of the matrix. It contains some Rows and Columns. This topic discusses various types of Matrices as Column Matrix, Row Matrix, Square Matrix, Identity Matrix, etc. The student will learn about the concept of equality of two matrices. It says that these will be equal if all corresponding elements are equal. Students will also learn different types of matrices such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices.
Another section of this chapter will explain important operations on matrices, such as the addition of matrices, multiplication of a matrix by a scalar, difference, and multiplication of matrices, etc. Also, it will explain various properties of matrices based on these operations. One important aspect of matrices is its transpose. It plays the main role to define and find the symmetric and skew-symmetric matrices.
Another important concept is the inverse of the matrix. This inverse matrix exists and gives the identity matrix after multiplying it with the original matrix. If the inverse of a matrix exists, then it will be unique. Students will also learn about the necessary conditions for matrices to have the inverse of them. Also, the student will see the methods to get an inverse matrix by performing elementary operations on the elements of a matrix. They learn the elementary operations on the inverse of a matrix.