**Become a Linear Algebra Master**

English | MP4 | AVC 1280×720 | AAC 48KHz 2ch | 15 Hours | 4.00 GB

Learn everything from Linear Algebra, then test your knowledge with 400+ practice questions

This course includes video and text explanations of everything from Linear Algebra, and it includes quizzes (with solutions!) and an additional workbooks with extra practice problems, to help you test your understanding along the way. Become a Linear Algebra Master is organized into the following sections:

What you’ll learn

- Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
- Operations on two matrices, including matrix multiplication and elimination matrices
- Matrices as vectors, including linear combinations and span, linear independence, and subspaces
- Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
- Matrix-vector products, including the null and column spaces, and solving Ax=b
- Transformations, including linear transformations, projections, and composition of transformations
- Inverses, including invertible and singular matrices, and solving systems with inverse matrices
- Determinants, including upper and lower triangular matrices, and Cramer’s rule
- Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
- Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
- Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process
- Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions

**Table of Contents**

**Getting started**

1 Hi! START HERE: Course overview

2 Download the formula sheet

**Operations on one matrix**

3 Introduction to operations on one matrix

4 RESOURCE: Quiz solutions for this section

5 Linear systems in two unknowns

6 Linear systems in two unknowns

7 Linear systems in three unknowns

8 Linear systems in three unknowns

9 Matrix dimensions and entries

10 Matrix dimensions and entries

11 Representing systems with matrices

12 Representing systems with matrices

13 Simple row operations

14 Simple row operations

15 Pivot entries and row-echelon forms

16 Pivot entries and row-echelon forms

17 Gauss-Jordan elimination

18 Gauss-Jordan elimination

19 Number of solutions to the linear system

20 Number of solutions to the linear system

21 BONUS! Extra practice problems. 🙂

**Operations on two matrices**

22 Introduction to operations on two matrices

23 RESOURCE: Quiz solutions for this section

24 Matrix addition and subtraction

25 Matrix addition and subtraction

26 Scalar multiplication

27 Scalar multiplication

28 Zero matrices

29 Zero matrices

30 Matrix multiplication

31 Matrix multiplication

32 Identity matrices

33 Identity matrices

34 The elimination matrix

35 The elimination matrix

36 BONUS! Extra practice problems. 🙂

**Matrices as vectors**

37 Introduction to matrices as vectors

38 RESOURCE: Quiz solutions for this section

39 Vectors

40 Vectors

41 Vector operations

42 Vector operations

43 Unit vectors and basis vectors

44 Unit vectors and basis vectors

45 Linear combinations and span

46 Linear combinations and span

47 Linear independence in two dimensions

48 Linear independence in two dimensions

49 Linear independence in three dimensions

50 Linear independence in three dimensions

51 Linear subspaces

52 Linear subspaces

53 Spans as subspaces

54 Spans as subspaces

55 Basis

56 Basis

57 BONUS! Extra practice problems. 🙂

**Dot products and cross products**

58 Introduction to dot products and cross products

59 RESOURCE: Quiz solutions for this section

60 Dot products

61 Dot products

62 Cauchy-Schwarz inequality

63 Cauchy-Schwarz inequality

64 Vector triangle inequality

65 Vector triangle inequality

66 Angle between vectors

67 Angle between vectors

68 Equation of a plane, and normal vectors

69 Equation of a plane, and normal vectors

70 Cross products

71 Cross products

72 Dot and cross products as opposite ideas

73 Dot and cross products as opposite ideas

74 BONUS! Extra practice problems. 🙂

**Matrix-vector products**

75 Introduction to matrix-vector products

76 RESOURCE: Quiz solutions for this section

77 Multiplying matrices by vectors

78 Multiplying matrices by vectors

79 The null space and Ax=O

80 The null space and Ax=O

81 Null space of a matrix

82 Null space of a matrix

83 The column space and Ax=b

84 The column space and Ax=b

85 Solving Ax=b

86 Solving Ax=b

87 Dimensionality, nullity, and rank

88 Dimensionality, nullity, and rank

89 BONUS! Extra practice problems. 🙂

**Transformations**

90 Introduction to transformations

91 RESOURCE: Quiz solutions for this section

92 Functions and transformations

93 Functions and transformations

94 Transformation matrices and the image of the subset

95 Transformation matrices and the image of the subset

96 Preimage, image, and the kernel

97 Preimage, image, and the kernel

98 Linear transformations as matrix-vector products

99 Linear transformations as matrix-vector products

100 Linear transformations as rotations

101 Linear transformations as rotations

102 Adding and scaling linear transformations

103 Adding and scaling linear transformations

104 Projections as linear transformations

105 Projections as linear transformations

106 Compositions of linear transformations

107 Compositions of linear transformations

108 BONUS! Extra practice problems. 🙂

**Inverses**

109 Introduction to inverses

110 RESOURCE: Quiz solutions for this section

111 Inverse of a transformation

112 Inverse of a transformation

113 Invertibility from the matrix-vector product

114 Invertibility from the matrix-vector product

115 Inverse transformations are linear

116 Inverse transformations are linear

117 Matrix inverses, and invertible and singular matrices

118 Matrix inverses, and invertible and singular matrices

119 Solving systems with inverse matrices

120 Solving systems with inverse matrices

121 BONUS! Extra practice problems. 🙂

**Determinants**

122 Introduction to determinants

123 RESOURCE: Quiz solutions for this section

124 Determinants

125 Determinants

126 Cramer’s rule for solving systems

127 Cramer’s rule for solving systems

128 Modifying determinants

129 Modifying determinants

130 Upper and lower triangular matrices

131 Upper and lower triangular matrices

132 Using determinants to find area

133 Using determinants to find area

134 BONUS! Extra practice problems. 🙂

**Transposes**

135 Introduction to transposes

136 RESOURCE: Quiz solutions for this section

137 Transposes and their determinants

138 Transposes and their determinants

139 Transposes of products, sums, and inverses

140 Transposes of products, sums, and inverses

141 Null and column spaces of the transpose

142 Null and column spaces of the transpose

143 The product of a matrix and its transpose

144 The product of a matrix and its transpose

145 BONUS! Extra practice problems. 🙂

**Orthogonality and change of basis**

146 Introduction to orthogonality and change of basis

147 RESOURCE: Quiz solutions for this section

148 Orthogonal complements

149 Orthogonal complements

150 Orthogonal complements of the fundamental subspaces

151 Orthogonal complements of the fundamental subspaces

152 Projection onto the subspace

153 Projection onto the subspace

154 Least squares solution

155 Least squares solution

156 Coordinates in a new basis

157 Coordinates in a new basis

158 Transformation matrix for a basis

159 Transformation matrix for a basis

160 BONUS! Extra practice problems. 🙂

**Orthonormal bases and Gram-Schmidt**

161 Introduction to orthonormal bases and Gram-Schmidt

162 RESOURCE: Quiz solutions for this section

163 Orthonormal bases

164 Orthonormal bases

165 Projection onto an orthonormal basis

166 Projection onto an orthonormal basis

167 Gram-Schmidt process for change of basis

168 Gram-Schmidt process for change of basis

169 BONUS! Extra practice problems. 🙂

**Eigenvalues and Eigenvectors**

170 Introduction to Eigenvalues and Eigenvectors

171 RESOURCE: Quiz solutions for this section

172 Eigenvalues, eigenvectors, eigenspaces

173 Eigenvalues, eigenvectors, eigenspaces

174 Eigen in three dimensions

175 Eigen in three dimensions

176 BONUS! Extra practice problems. 🙂

**Final exam and wrap-up**

177 Linear Algebra final exam

178 Wrap-up

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