#### 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