Linear Algebra - MAT223 Workbook

Lessons Module 1 – Sets, Vectors & Notation The Magic Carpet Ride 1 The Magic Carpet Ride, Hide and Seek 2 3 4 5 6 7 8 Module 2 – Sets of Vectors, Lines & Planes 9 10 11 12 13 14 Module 3 – Spans, Translated Spans, and Linear Independence/Dependence 15 16 17 The Magic Carpet Ride, Getting Back Home 18 19 20 21 22 Linear Independence and Dependence, Creating Examples 23 Module 4 – Dot Products & Normal Forms 24 25 26 27 28 29 Module 5 – Projections & Vector Components 30 31 32 33 Module 6 – Subspaces & Bases 34 35 36 Module 7 – Matrix Representations of Systems of Linear Equations 37 38 39 40 Module 8 – Coordinates & Change of Basis I 41 42 43 Module 9 – Linear Transformations Italicizing N 44 Beyond the N 45 46 47 48 Module 10 – The Composition of Linear Transformations Pat and Jamie 49 50 Module 11 – Range & Nullspace of a Linear Transformation 51 52 53 54 55 56 57 58 59 60 61 62 Module 12 – Inverse Functions & Inverse Matrices Getting back N 63 64 65 66 67 68 Module 13 – Change of Basis II 69 70 71 Module 14 – Determinants 72 73 74 75 76 77 78 79 80 81 Module 15 – Eigenvalues and Eigenvectors The Green and the Black 82 83 84 85 86 87 Module 16 – Diagonalization 88 89 90 91 Appendix 1 – Systems of Linear Equations I Appendix 2 – Systems of Linear Equations II Appendix 3 – Matrices & Matrix Operations Appendix 4 – Formulas for 2×2 and 3×3 Determinants Appendix 5 – Practice Problem Solutions Solutions for Module 1 Solutions for Module 2 Solutions for Module 3 Solutions for Module 4 Solutions for Module 5 Solutions for Module 6 Solutions for Module 7 Solutions for Module 8 Solutions for Module 9 Solutions for Module 10 Solutions for Module 11 Solutions for Module 12 Solutions for Module 13 Solutions for Module 14 Solutions for Module 15 Solutions for Module 16 Solutions for Appendix 1 Solutions for Appendix 2 Solutions for Appendix 3 Solutions for Appendix 4 Indices – Indices