Matrices and Geometry

UNIT 1: SYSTEM OF LINEAR & MATRIX EQUATIONS 1.0 OBJECTIVES 1.1 INTRODUCTION 1.2 SYSTEM OF LINEAR EQUATIONS 1.3 ROW REDUCTIONS AND ECHELON FORMS 1.4 VECTOR EQUATIONS 1.5 THE MATRIX EQUATION Ax = b 1.6 SOLUTION SETS OF LINEAR SYSTEMS 1.7 LINEAR INDEPENDENCE 1.8 THE RANK OF A MATRIX AND APPLICATION 1.9 THE MATRIX OF A LINEAR TRANSFORMATION 1.10 CHARACTERIZATION OF INVERTIBLE MATRICES 1.11 APPLICATION TO COMPUTER GRAPHICS 1.12 EIGENVECTORS AND EIGENVALUES 1.13 THE CHARACTERISTIC EQUATION AND CAYLOY HAMILTON THEOREM UNIT 2: GEOMATRICAL OF COMPLEX NUMBER AND FUNDAMENTAL THEOREM OF ALGERBRA 2.0 OBJECTIVES 2.1 INTRODUCTION 2.2 GEOMETRICAL REPRESENTATION OF ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF COMPLEX NNUMBERS 2.3 LINES HALF PLANES, CIRCLES, DISCS IN TERM OF COMPLEX VARIABLES 2.4 STATEMENT OF THE FUNDAMENTAL THEOREM OF ALGERBRA AND ITS CONSEQUENCES 2.5 DE MOIVRE'S THEOREM FOR RATIONAL INDICES AND ITS SIMPLE APPLICATION UNIT 3: PARABOLA, ELLIPSE AND HYPERBOLA 3.0 OBJECTIVES 3.1 INTRODUCTION 3.2 TECHNIQUES FOR SKETCHING PARABOLA, ELLIPSE AND HYPERBOLA 3.3 REFLECTION PROPERTIES OF ELLIPSE, PARABOLA, HYPERBOLA 3.4 CLASSIFICATION OF QUADRATIC EQUATIONS REPRESENTING LINES, PARABOLA, ELLIPSE AND HYPERBOLA 3.5 DIFFERENTIATIONS OF VECTORE VALUED FUNCTION, GRADIENT, DIVERGENCE, CURL UNIT 4: SPHERES AND CYLINDERICAL SURFACES 4.0 OBJECTIVES 4.1 INTRODUCTION 4.2 SPHERE 4.3 CYLINDRICAL SURFACES 4.4 ILLUSTRATION OF GRAPHING STANDARD QUADRIC SURFACES LIKE CONE, ELLIPSOID