In Mathematics, the matrix is an important term introduced by the 19th-century mathematician James Sylvester. In the 1850s, another mathematician Arthur Cayley developed the algebraic aspect of matrix. This concept was used for the study of systems of linear equations. As far as the JEE Main is concerned, this is a very significant topic. This is a topic which students should practise and learn. Revising the previous years’ questions on matrix will help students to get an idea about the pattern of the exam and also improve the speed of cracking the problems. If the concept is clear, it will be very easy for the students to solve the matrix problems.
We can define a matrix as a rectangular arrangement of real or complex numbers in m rows and n columns. Matrices have a wide range of applications in geometry and algebra. A matrix can be represented by K = [kij] mxn. Here k11, k12, ….. etc., are known as the elements of matrix K, where kij belongs to the ith row and jth column and is called the (i, j)th element of the matrix K = [kij]. Matrix is used to express properties and operations of abstract linear algebra. For example, matrix multiplication denotes the composition of linear maps.
Types of Matrices
The different types of matrices are given below:
- Symmetric matrix
- Identity matrix
- Skew symmetric matrix
- Hermitian and skew hermitian matrix
- Idempotent matrix
- Involuntary matrix
- Orthogonal matrix
Consider matrix A and B. We can add or subtract A and B if both are of the same size. Addition is commutative in matrix addition, while subtraction is not commutative. To perform a multiplication operation, the number of columns in the first matrix and the number of rows in the second matrix should be the same.
Transpose of a Matrix
We can obtain the transpose of a matrix by interchanging the rows and columns. The transpose of matrix A is denoted by AT. The transpose of AT is equal to A. i.e (AT)T = A.
Matrix is used for plotting graphs and to do scientific research in different fields. These can also be used to represent real-world data like the population of people, infant mortality rate, etc. These are considered as the best representation methods for plotting surveys. In the field of engineering, the matrix has vast applications. These are used to solve problems related to dynamics, equations of motions, to calculate velocity, displacement and drifts of functions.
Determinant is a scalar value obtained from a square matrix. If we change the rows and columns of a determinant, the value of the determinant remains unchanged. The development of determinants happened while scientists were trying to solve the system of linear equations. If any two rows or columns of a determinant are interchanged, then the sign will be changed.
JEE aspirants are advised to revise and learn the previous years’ questions on the matrix and determinant so that they can be familiar with the pattern and difficulty level. Log on to BYJU’S for important formulas pdf, and solutions of previous years’ JEE question papers.