CONTENTS

CONTENTS - - vi E- Book Assessment Applications of Differentiation - . Applications of Differentiation in Business and Economics October . Maxima and Minima . Applications of Maxima and Minima . Partial Derivatives . Applications of Partial Derivatives Financial Mathematics - . Annuities October . Stocks, Shares, Debentures and Brokerage Descriptive Statistics and Probability - . Measures of Central Tendency November . Measures of Dispersion . Probability Correlation and Regression Analysis - . Correlation November . Rank Correlation . Regression Analysis Operations Research - . Linear Programming Problem December . Network Analysis Answers - Tables - Books for Reference As the Statistics component of this text book involves problems based on numerical calculations, Business Mathematics and Statistics students are advised to use calculator - - Matrices and Determinants Seki Kowa . Determinants Introduction The idea of a determinant was believed to be originated from a Japanese Mathematician Seki Kowa ( ) while systematizing the old Chinese method of solving simultaneous equations whose coefficients were represented by calculating bamboos or sticks. Later the German Mathematician Gottfried Wilhelm Von Leibnitz formally developed determinants. The present vertical notation was given in by Arthur Cayley. Determinant was invented independently by Crammer whose well known rule for solving simultaneous equations was published in . In class X, we have studied matrices and algebra of matrices. We have also learnt that a system of algebraic equations can be expressed in the form of matrices. We know that the area of a triangle with vertices ( x , y ) ( x , y ) and ( x , y ) is x y x y x y @ To minimize the difficulty in remember­ing this type of expression, Mathematicians developed the idea of representing the expression in determinant form and the above expression can be represented in the form Thus a determinant is a particular type of expression written in a special concise form. Note that the quantities are arranged in the form of a square between two vertical lines. This arrangement is