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DETERMINANTS - NCERT
76 MATHEMATICSvAll Mathematical truths are relative and conditional. STEINMETZ IntroductionIn the previous chapter, we have studied about matricesand algebra of matrices. We have also learnt that a systemof algebraic equations can be expressed in the form ofmatrices. This means, a system of linear equations likea1 x + b1 y =c1a2 x + b2 y =c2can be represented as 111222abcxabcy = . Now, thissystem of equations has a unique solution or not, isdetermined by the number a1 b2 a2 b1. (Recall that if1122abab or, a1 b2 a2 b1 0, then the system of linearequations has a unique solution). The number a1 b2 a2 b1which determines uniqueness of solution is associated with the matrix 1122 Aabab = and is called the determinant of A or det A. DETERMINANTS have wide applications inEngineering, Science, Economics, Social Science, this chapter, we shall study DETERMINANTS up to order three only with real , we will study various properties of DETERMINANTS , minors, cofactors and applicationsof 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 linearequations in two or three variabl
vAll Mathematical truths are relative and conditional. — C.P. STEINMETZ v 4.1 Introduction In the previous chapter, we have studied about matrices and algebra of matrices. We have also learnt that a system of algebraic equations can be expressed in the form of matrices.
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