Also, we will study various properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle, adjoint and inverse of a square matrix, consistency and inconsistency of system of linear equations and solution of linear equations in two or three variables using inverse of a matrix. 4.2 Determinant Learn what determinants are, how to calculate them for matrices of different orders, and how to use them for finding area, inverse and adjoint of a matrix. This web page covers the basics of determinants with definitions, properties, examples and exercises from NCERT textbook. Determinants are defined as a scalar value which is obtained by functions of elements of a square matrix. It helps solve various algebraic calculations in very simple ways.Determinants help us determine the uniqueness of solutions in the matrix. Determinants and matrices, in linear algebra, are used to solve linear equations by applying Cramer’s rule to a set of non-homogeneous equations which are in linear form. Determinants are calculated for square matrices only. If the determinant of a matrix is zero, it is called a singular determinant and if it is one, then it is known as unimodular. For the system of equations to have a unique solution, the determinant of the matrix must be nonsingular, that is its value must be nonzero. In ...
