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Master Chapter 4 Class 12 ... 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 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 are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of linear equations has a unique solution iff the determinant of the system's matrix is nonzero (i.e., the matrix is nonsingular).
