iii MAT1503/1
CONTENTS
Page
PREFACE v
Introduction v
Prescribed Book vii
Overview of the Module vii
Study Guide ix
Learning Strategies for Mathematics; and in particular for this Module x
Assessment xii
CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES 1...
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iii MAT1503/1
CONTENTS
Page
PREFACE v
Introduction v
Prescribed Book vii
Overview of the Module vii
Study Guide ix
Learning Strategies for Mathematics; and in particular for this Module x
Assessment xii
CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES 1
1.
1 Introduction to Systems of Linear Equations 2
1.
2 Gaussian Elimination 6
1.
3 Matrices and Matrix Operations 19
1.
4 Inverses; Rules of Matrix Arithmetic 22
1.
5 Elementary Matrices and a Method for Finding the Inverse of A 24
1.
6 Further Results on Systems of Equations and Invertibility 28
1.
7 Diagonal, Triangular, and Symmetric Matrices 30
Review of Chapter 1 31
CHAPTER 2 DETERMINANTS 33
2.
1 Determinants by Cofactor Expansion 34
2.
2 Evaluating Determinants by Row Reduction 36
2.
3 Properties of the Determinant Function 39
Review of Chapter 2 43
CHAPTER 3 VECTORS IN 2-SPACE AND 3-SPACE 45
3.
1 Introduction to Vectors 46
3.
2 Norm of a Vector; Vector Arithmetic 50
3.
3 Dot Product; Projections 51
3.
4 Cross Product 53
3.
5 L
Less
