Section 1 : Getting started

Lecture 1 Hi! START HERE Course overview 1:24
Lecture 2 Download the formula sheet Text
Lecture 3 The EVERYTHING download Text

Section 2 : Operations on one matrix__

Lecture 4 Introduction to operations on one matrix 1:19
Lecture 5 RESOURCE Quiz solutions for this section Text
Lecture 6 Linear systems in two unknowns Text
Lecture 7 Linear systems in two unknowns 12:16
Lecture 8 Linear systems in three unknowns Pdf
Lecture 9 Linear systems in three unknowns 10:20
Lecture 10 Matrix dimensions and entries Pdf
Lecture 11 Matrix dimensions and entries 6:7
Lecture 12 Representing systems with matrices Pdf
Lecture 13 Representing systems with matrices 9:58
Lecture 14 Simple row operations Pdf
Lecture 15 Simple row operations 10:14
lecture 16 Pivot entries and row-echelon forms Pdf
Lecture 17 Pivot entries and row-echelon forms 16:18
Lecture 18 Gauss-Jordan elimination Pdf
Lecture 19 Gauss-Jordan elimination 13:57
Lecture 20 Number of solutions to the linear system Pdf
Lecture 21 Number of solutions to the linear system 13:20
Lecture 22 BONUS! Extra practice problems. Text

Section 3 : Operations on two matrices__

Lecture 23 Introduction to operations on two matrices 1:11
Lecture 24 RESOURCE Quiz solutions for this section Text
Lecture 25 Matrix addition and subtraction Pdf
Lecture 26 Matrix addition and subtraction 9:48
Lecture 27 Scalar multiplication Pdf
Lecture 28 Scalar multiplication 6:5
Lecture 29 Zero matrices Pdf
Lecture 30 Zero matrices 4:7
Lecture 31 Matrix multiplication Pdf
Lecture 32 Matrix multiplication
Lecture 33 Identity matrices Pdf
Lecture 34 Identity matrices 9:24
Lecture 35 The elimination matrix Pdf
Lecture 36 The elimination matrix 13:19
Lecture 37 BONUS! Extra practice problems Text

Section 4 : Matrices as vectors__

Lecture 38 Introduction to matrices as vectors 1:12
Lecture 39 RESOURCE Quiz solutions for this section Text
Lecture 40 Vectors Pdf
Lecture 41 Vectors 8:54
Lecture 42 Vector operations Pdf
Lecture 43 Vector operations 10:49
Lecture 44 Unit vectors and basis vectors Pdf
Lecture 45 Unit vectors and basis vectors 16:10
Lecture 46 Linear combinations and span Pdf
Lecture 47 Linear combinations and span 13:28
Lecture 48 Linear independence in two dimensions Pdf
Lecture 49 Linear independence in two dimensions 13:55
Lecture 50 Linear independence in three dimensions Pdf
Lecture 51 Linear independence in three dimensions 9:38
Lecture 52 Linear subspaces Pdf
Lecture 53 Linear subspaces 13:39
Lecture 54 Spans as subspaces Pdf
Lecture 55 Spans as subspaces 9:22
Lecture 56 Basis Pdf
Lecture 57 Basis 17:15
Lecture 58 BONUS! Extra practice problems Text

Section 5 : Dot products and cross

Lecture 59 Introduction to dot products and cross product 1:6
Lecture 60 RESOURCE Quiz solutions for this section Text
Lecture 61 Dot products Pdf
Lecture 62 Dot products 10:35
Lecture 63 Cauchy-Schwarz inequality Pdf
Lecture 64 Cauchy-Schwarz inequality 8:5
Lecture 65 Vector triangle inequality Pdf
Lecture 66 Vector triangle inequality 10:27
Lecture 67 Angle between vectors Pdf
Lecture 68 Angle between vectors 9:5
Lecture 69 Equation of a plane, and normal vectors Pdf
Lecture 70 Equation of a plane, and normal vectors 9:10
Lecture 71 Cross products Pdf
Lecture 72 Cross products 14:24
Lecture 73 Dot and cross products as opposite ideas Pdf
Lecture 74 Dot and cross products as opposite ideas 13:38
Lecture 75 BONUS! Extra practice problems Text

Section 6 : Matrix-vector products

Lecture 76 Introduction to matrix-vector products 1:3
Lecture 77 RESOURCE Quiz solutions for this section Text
Lecture 78 Multiplying matrices by vectors Pdf
Lecture 79 Multiplying matrices by vectors 8:32
Lecture 80 The null space and Ax=O Pdf
Lecture 81 The null space and Ax=O 20:25
Lecture 82 Null space of a matrix Pdf
Lecture 83 Null space of a matrix 16:21
Lecture 84 The column space and Ax=b Pdf
Lecture 85 The column space and Ax=b 17:17
Lecture 86 Solving Ax=b Pdf
Lecture 87 Solving Ax=b 16:46
Lecture 88 Dimensionality, nullity, and rank Pdf
Lecture 89 Dimensionality, nullity, and rank 9:40
Lecture 90 BONUS! Extra practice problems Text

Section 7 : Transformations

Lecture 91 Introduction to transformations 1:16
Lecture 92 RESOURCE Quiz solutions for this section Text
Lecture 93 Functions and transformations Pdf
Lecture 94 Functions and transformations 12:42
Lecture 95 Transformation matrices and the image of the Pdf
Lecture 96 Transformation matrices and the image of the
Lecture 97 Preimage, image, and the kernel Pdf
Lecture 98 Preimage, image, and the kernel 10:16
Lecture 99 Linear transformations as matrix-vector produ Pdf
Lecture 100 Linear transformations as matrix-vector produ 14:49
Lecture 101 Linear transformations as rotations Pdf
Lecture 102 Linear transformations as rotations 5:49
Lecture 103 Adding and scaling linear transformations Pdf
Lecture 104 Adding and scaling linear transformations
Lecture 105 Projections as linear transformations Pdf
Lecture 106 Projections as linear transformations 15:52
Lecture 107 Compositions of linear transformations Pdf
Lecture 108 Compositions of linear transformations 10:0
Lecture 109 BONUS! Extra practice problems. Text

Section 8 : Inverses

Lecture 110 Introduction to inverses 1:21
Lecture 111 RESOURCE Quiz solutions for this section Text
Lecture 112 Inverse of a transformation Pdf
Lecture 113 Inverse of a transformation 14:39
Lecture 114 Invertibility from the matrix-vector product Pdf
Lecture 115 Invertibility from the matrix-vector product. 16:24
Lecture 116 Inverse transformations are linear Pdf
Lecture 117 Inverse transformations are linear 9:54
Lecture 118 Matrix inverses, and invertible and singular Pdf
Lecture 119 Matrix inverses, and invertible and singular 11:37
Lecture 120 Solving systems with inverse matrices Pdf
Lecture 121 Solving systems with inverse matrices 8:40
Lecture 122 BONUS! Extra practice problems Text

Section 9 : Determinants

Lecture 123 Introduction to determinants 0:49
Lecture 124 RESOURCE Quiz solutions for this section Text
Lecture 125 Determinants Pdf
Lecture 126 Determinants 20:22
Lecture 127 Cramer's rule for solving systems Pdf
Lecture 128 Cramer's rule for solving systems 15:47
Lecture 129 Modifying determinants Pdf
Lecture 130 Modifying determinants 9:53
Lecture 131 Upper and lower triangular matrices Pdf
Lecture 132 Upper and lower triangular matrices 17:0
Lecture 133 Using determinants to find area Pdf
Lecture 134 Using determinants to find area 8:28
Lecture 135 BONUS! Extra practice problems. ) Text

Section 10 : Transposes

Lecture 136 Introduction to transposes 0:52
Lecture 137 RESOURCE Quiz solutions for this section Text
Lecture 138 Transposes and their determinants Pdf
Lecture 139 Transposes and their determinants 9:14
Lecture 140 Transposes of products, sums, and inverses Pdf
Lecture 141 Transposes of products, sums, and inverses
Lecture 142 Null and column spaces of the transpose Pdf
Lecture 143 Null and column spaces of the transpose 21:22
Lecture 144 The product of a matrix and its transpose Pdf
Lecture 145 The product of a matrix and its transpose 7:4
Lecture 146 BONUS! Extra practice problems Text

Section 11 : Orthogonality and change

Lecture 147 Introduction to orthogonality and change of b 1:24
Lecture 148 RESOURCE Quiz solutions for this section Text
Lecture 149 Orthogonal complements Pdf
Lecture 150 Orthogonal complements 15:35
Lecture 151 Orthogonal complements of the fundamental Pdf
Lecture 152 Orthogonal complements of the fundamental sub 15:49
Lecture 153 Projection onto the subspace Pdf
Lecture 154 Projection onto the subspace 18:36
Lecture 155 Least squares solution Pdf
Lecture 156 Least squares solution 18:53
Lecture 157 Coordinates in a new basis
Lecture 158 Coordinates in a new basis Pdf
Lecture 159 Transformation matrix for a basis Pdf
Lecture 160 Transformation matrix for a basis 14:35
Lecture 161 BONUS! Extra practice problems. Text

Section 12 : Orthonormal bases

Lecture 162 Introduction to orthonormal bases and Gram-Sc 1:2
Lecture 163 RESOURCE Quiz solutions for this section Text
Lecture 164 Orthonormal bases Pdf
Lecture 165 Orthonormal bases 9:49
Lecture 166 Projection onto an orthonormal basis Pdf
Lecture 167 Projection onto an orthonormal basis 9:6
Lecture 168 Gram-Schmidt process for change of basis Pdf
Lecture 169 Gram-Schmidt process for change of basis 16:56
Lecture 170 BONUS! Extra practice problems. Text

Section 13 : Eigenvalues and Eigenvectors

Lecture 171 Introduction to Eigenvalues and Eigenvectors. 0:50
Lecture 172 RESOURCE Quiz solutions for this section Text
Lecture 173 Eigenvalues, eigenvectors, eigenspaces Pdf
Lecture 174 Eigenvalues, eigenvectors, eigenspaces 21:33
Lecture 175 Eigen in three dimensions Pdf
Lecture 176 Eigen in three dimensions 16:10
Lecture 177 BONUS! Extra practice problems. Text

Section 14 : Final exam and wrap-up

Lecture 178 Practice final exam #1 (optional) Text
Lecture 179 Practice final exam #2 (optional) Text
Lecture 180 Linear Algebra final exam Text
Lecture 181 Wrap-up 0:20