Linear Algebra All Contents
347 videos • 4,107 views • by Fatemeh Yarahmadi
1
Linear Algebra in 24 hours- Definition of Linear Equation in n variable
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2
Linear Algebra in 24 hours. Definition of solution set (Enjoy Light Music)
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3
Linear Algebra in 24 hours- Parametric representation and particular solution 3x+2y-z=3
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4
Linear Algebra in 24 hours- Definition of System of Linear Equations
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5
Linear Algebra in 24 hours- Definition of Consistent and inconsistent System of Linear Equations
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6
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7
Linear Algebra in 24 hours- Equivalent Systems and Row Echelon Form Example
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8
Linear Algebra HW Video Solution-Systems of Linear Equations-Identify Linear and Nonlinear Equations
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9
Linear Algebra HW Video Solution-Systems of Linear Equations- Parametric Representation
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10
Why Linear Algebra?
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11
What is a matrix? What are the entries of a matrix?
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12
Solve a system of equations using Elementary Row Operations- Echelon Form
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13
Solve a system of equations using Elementary Row Operations- Gaussian Elimination
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14
Solve a system of equations using Elementary Row Operations- System with No Solution
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15
Solve a system of equations using Elementary Row Operations- System with Many Solutions
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16
Linear Algebra HW Solution Gaussian Elimination Q15
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17
Linear Algebra HW Solution Gaussian Elimination Q25
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18
Linear Algebra HW Solution Homogeneous System Q45
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19
Linear Algebra- Equality between matrices
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20
Linear Algebra- Addition of two matrices
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21
Linear Algebra- Subtracting Matrices
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22
Linear Algebra- Scalar Multiplication of Matrices
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23
Matrices Multiplication Formula
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24
Linear Algebra- Matrix Multiplication Example
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25
Linear Algebra- Matrix Multiplication more examples
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26
Linear Algebra- System of Linear Equations in Matrix Form
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27
Linear Algebra- System of Linear Equations in Matrix Form
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28
Linear Algebra- Commutative property of matrix addition
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29
Linear Algebra- Commutative property of matrix multiplication? Remember this example (contradiction)
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30
Linear Algebra- Associative Property for addition and multiplication, not subtraction!
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31
Linear Algebra- Example of associate property of matrix multiplication
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32
Linear Algebra- In general If AC=BC then A=B?
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33
Linear Algebra- All about identity matrices
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34
Linear Algebra- What is the transpose of a matrix? Some examples.
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35
Exam Review- Linear Algebra- Which one is linear?
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36
Exam Review- Linear Algebra- Find Parametric Representation of Solution
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37
Exam Review- Linear Algebra- Solve system using Augmented Matrix
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38
Exam Review- Linear Algebra- Convert Matrix to system of equations
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39
Exam Review- Linear Algebra- Solve System of three equations and three variables
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40
Homework- Linear Algebra- Adding Matrices
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41
Homework- Linear Algebra- Scalar Multiplication
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42
Homework- Linear Algebra- Scalar Multiplication with Matrices Multiplication
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43
Homework 2.1 Q50- Linear Algebra- write the column matrix b as linear combination of columns of A
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44
Homework 2.2 Q50- Linear Algebra- Diagonal Matrix to different exponents
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45
Linear Algebra- symmetric and asymmetric matrices
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46
Linear Algebra- Invertible Matrix
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47
Linear Algebra- Check if two matrices are inverse of each other
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48
Linear Algebra- Find the inverse of a matrix using adjoining matrix and Gauss Jordan Elimination
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49
Linear Algebra- Find Inverse of a 3 by 3 matrix using adjoining matrix
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50
Linear Algebra- Find Inverse of a 2 by 2 matrix using adjoining matrix and formula
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51
Linear Algebra- Transpose and Inverse of Matrices Rules
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52
Linear Algebra- Solve a system of linear equations using Inverse of coefficient matrix
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53
Linear Algebra- HW 2.3 Q55- Find x such that matrix is nonsingular
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54
Linear Algebra- HW 2.3 Q60- Find inverse of matrix with trigonometric entries
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55
Linear Algebra- What is an elementary matrix?
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56
Linear Algebra- Definition of row equivalent matrices
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57
Linear Algebra- Write matrix A as the product of elementary matrices
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58
Linear Algebra- What is LU Factorization
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59
Linear Algebra- If A is a nilpotent matrix then I-A is invertible- Proof
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60
Nilpotent Matrix with example
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61
Linear Algebra- Determinant of a 3 by 3 matrix with two expansions (along row and along column)
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62
Determinant of a 4 by 4 matrix with two expansions (along column with most zeroes)
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63
Linear Algebra- Determinant of a 4 by 4 Triangular matrix with two methods
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64
Linear Algebra- Elementary row operation and determinant (interchange two rows)
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65
Linear Algebra- Elementary row operation and determinant Example
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66
Linear Algebra- Determinant using Elementary Column Operation
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67
Linear Algebra- If I-AB is nonsingular then so as I-BA
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68
Linear Algebra- Find Elementary Matrix E such that EA=B
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69
Linear Algebra- True or False? The identity matrix is an elementary matrix.
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70
Linear Algebra- True or False? The zero matrix is an elementary matrix.
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71
Linear Algebra- True or False? Nonsingular matrix can be written as product of elementary matrices.
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72
Linear Algebra- True or False? Ax = 0 has only the trivial solution iff
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73
Linear Algebra- Definition of Idempotent Matrix and example
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74
Linear Algebra- A is idempotent if and only if its transpose is idempotent
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75
Linear Algebra- Any nonsingular (invertible) idempotent matrix is identity matrix
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76
Linear Algebra- Cramer's Rule for a System with two equations and Two Variables
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77
Linear Algebra- Equation of Plane Using Determinant
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78
Linear Algebra- Area of Triangle using determinant
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79
Linear Algebra- What makes a set a vector space?
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80
Linear Algebra- Basic Examples of Vector Space
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81
Linear Algebra- What is a field, and some examples
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82
Linear Algebra- Set of Integers is a commutative group
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83
Linear Algebra- Nonzero Rationals is a group
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84
Linear Algebra- Vector Space on a field F - The set of n-tuples
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85
Linear Algebra- Vector Space of all mxn matrices
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86
Linear Algebra- Vector Space of all functions mapping S to F
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87
Linear Algebra- Vector Space of all Sequences
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88
Linear Algebra- Vector Space of all Polynomials
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89
Linear Algebra- Not a Vector Space (Remember me!)
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90
Linear Algebra- HW 4.2 Find Zero Vector or Additive Identity
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91
Linear Algebra- HW 4.2 Find Additive Inverse
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92
Linear Algebra- HW 4.2 Set of polynomials of degree 3 is not a vector space
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93
Linear Algebra- What is a subspace? Trivial Subspaces
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94
Linear Algebra- Subspace of Space
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95
Linear Algebra- Subspace - All symmetric matrices
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96
Linear Algebra- Not a Subspace - All singular matrices
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97
Linear Algebra- Subspaces of Functions
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98
Linear Algebra- Intersection of Subspaces is a Subspace
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99
Linear Algebra- Linear Combination
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100
Linear Algebra- S spans V- Example of Space
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101
Linear Algebra- S spans V- Example polynomials of degree less than or equal 3
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101
Linear Algebra- S spans V- Example polynomials of degree less than or equal 3
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102
Linear Algebra- Span of a Set
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103
Linear Algebra- span(S) is subspace of V
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104
[Private video]
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105
[Private video]
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106
Linear Algebra- Standard Basis for Space
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107
Linear Algebra- NonStandard Basis for Space
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108
Linear Algebra- Basis for Polynomial Space and M2,2 Space
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109
Linear Algebra- Dimension for Spaces with example of Diagonal Matrices
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110
Linear Algebra- Empty Set is Independent and Basis for Zero Vector Space
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111
Find the dimension of subspace of R^3 W={(d,c-d,c)I c,d are real numbers}
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112
Find the dimension of subspace of R4
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113
Linear Algebra- Dimension of symmetric matrices of size 2
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114
Linear Algebra- Row Vectors and Column Vectors
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115
Linear Algebra- Definition of Row Space and Column Space
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116
Linear Algebra- Find a basis for the row space of a Matrix using Row Echelon Form
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117
Linear Algebra- Find the rank of a Matrix
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118
Find the dimension of subspace of R^3 W={(2b,b,0), b is a real number}
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119
Linear Algebra- Find the nullity of a matrix
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120
Linear Algebra- Rank of a Matrix (then we find the nullity)
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121
Linear Algebra- Sketch of proof- n=rank (A)+ nullity (A)
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122
Linear Algebra- Particular Solution and General Solution
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123
Linear Algebra- Ax=b is Consistent iff b is in Column Space of A
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124
Linear Algebra- Some Notes on the Rank part 1
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125
Linear Algebra- Some Notes on the Rank part 2
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126
Linear Algebra- Some Notes on the Dimension
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127
Linear Algebra- Coordinate Representation Relative to a Basis Example 1
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128
Linear Algebra- Finding a Coordinate Matrix Example
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129
Linear Algebra- Finding a Coordinate Matrix Relative to a Nonstandard Basis
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130
Linear Algebra- Transition Matrix between two bases
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131
Linear Algebra- Norm of a vector
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132
Linear Algebra- Unit Vector
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133
Linear Algebra- Distance Between Two Vectors
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134
Linear Algebra- Properties of Dot Product
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135
Linear Algebra- Creative Proof of Cauchy Schwarz Inequality for Vectors
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136
Linear Algebra- Triangle Inequality Proof
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137
Linear Algebra- Definition of Orthogonal Vectors
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138
Linear Algebra- An Extension of Pythagorean Theorem Using Triangle Inequality
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139
Linear Algebra- Inner Product Space
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140
Linear Algebra- Define an Inner Product on Plane
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141
Linear Algebra- Not an Inner Product
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142
Linear Algebra- Inner Product on Space of 2x2 Matrices
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143
Linear Algebra- Inner Product on Space of Continuous Functions
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144
Linear Algebra- Linear Transformation
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145
Linear Algebra- Not a Linear Transformation
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146
Linear Algebra- Properties of Linear Transformation with Example
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147
Linear Algebra- Linear Transformation using Integral and Matrix
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148
Linear Algebra- Linear Transformation and Rotation
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149
Linear Algebra- Differential Operator
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150
Linear Algebra- Kernel of a Linear Transformation
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151
Linear Algebra- Kernel of a Linear Transformation Example 1
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152
Linear Algebra- Kernel and Range of a Linear Transformation Example 1
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153
Linear Algebra- Kernel and Range of a Linear Transformation Example 2
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154
Linear Algebra- Vector Space of all Linear Transformations
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155
Linear Algebra- Vector Space of all Linear Transformations and Their Operations
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156
Linear Algebra- Vector Space of all Linear Transformations and Addition and Composition
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157
Linear Algebra- Finding a Standard Matrix for a Linear Transformation
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158
Linear Algebra HW 4.6 Q5: Find a basis for row space and column space of matrix A
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159
Linear Algebra HW 4.6 Q10 Find the Rank and Basis for the Row Space of Matrix A
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160
Linear Algebra HW 4.6 Q15 Find a Basis for the Subspace of R3 Spanned by S.
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161
Linear Algebra HW 4.6 Q20 Find a basis for the subspace spanned by S
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162
Linear Algebra HW 4.6 Q25 Find a basis for the Column Space
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163
Linear Algebra HW 4.6 Q30 Find NullSpace of 3x1 Matrix
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164
Linear Algebra HW 4.6 Q41 Find the rank and Nullity of a 4x5 matrix
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165
Linear Algebra Exam Practice: The rank of product of two matrices can be less than the rank of each
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166
Linear Algebra Exam Practice: Nonzero row vectors of a matrix are Linearly Independent
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167
Linear Algebra Exam Practice Find matrices that rank (A+B) is less than rank of each A and B
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168
Linear Algebra Exam Practice Rank of A and relation with the dimension of A
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169
Linear Algebra Exam Practice Nullity of A is subset of Nullity of A^TA
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170
Linear Algebra- What is Eigenvalue and Eigenvector
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171
Linear Algebra- Find Eigenvalue Corresponding to Eigenvector x
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172
Linear Algebra- Use Characteristic Polynomial to find Eigenvalues
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173
Linear Algebra- Use Characteristic Polynomial to find Eigenvalues then their eigenvectors
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174
Linear Algebra- Dimension of the Eigenspace
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175
Linear Algebra- Orthogonal and Orthonormal
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176
Linear Algebra- Orthogonal Projection of u onto v
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177
Linear Algebra- Orthogonal Projection of f(x)=1 onto g(x)=x
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178
Linear Algebra- Gram Schmidt Method
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179
Linear Algebra- Kernel of Zero Transformation
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180
Linear Algebra- Kernel of Identity Transformation
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181
Linear Algebra- Kernel of Transformation mapping (x,y) to (x-2y, 0, -y)
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182
Linear Algebra- Kernel of Transformation T(x)=Ax
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183
Linear Algebra- Basis for the Kernel of Transformation T(x)=Ax
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184
Linear Algebra- Basis for the Range of Transformation T(x)=Ax
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185
Linear Algebra- Example of the sum of the nullity and rank equal to the dimension of the domain
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186
Linear Algebra- Show that T is one to one Transformation T(x)=Ax
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187
Linear Algebra- Show that a Transformation T(x)=Ax is Onto- Rank(T)=Dim(W)- Isomorphism
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188
[Private video]
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189
Linear Algebra and Self Driving Cars
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190
Linear Equation in n Variables with Example
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191
Nonlinear Equations with Example in Linear Algebra
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192
Solution of a Linear Equation Using Parameter
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193
What is a system of Linear Equations?
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194
#Consistent and #Inconsistent Systems Example 1
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195
Row Echelon Form and Back Substitution in Example 1
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196
Row Echelon Form and Back Substitution Example 2
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197
Solving a System of Equation Using Elimination To Rewrite in Row Echelon Form
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198
Row Echelon Form- Inconsistent System
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199
Determine whether the equation is linear in the variables x and y.
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200
Determine if the equation is linear in the variables x and y.
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201
Find a parametric representation of the solution set of the linear equation
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202
Graph the system of linear equations. Solve the system and interpret your answer.
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203
Use back-substitution to solve the system.
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