Linear Algebra and Differential Equations Part 1 math 227
math 227 part 1
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CHAPTER 1 System of Linear Equation and Matrices
- 1.1 Linear Equation 11:41
- 1.1 Solution of System of Linear Equations 13:56
- 1.1 Introduction to Matrices 06:31
- 1.1 Type of Matrices 10:32
- 1.1 Augmented Matrix 07:40
- 1.1 Elementary Row Operation 08:05
- 1.1 Extra Example 02:41
- 1.1 Solving Linear system (with unique solution) 13:52
- 1.1 Example 1 08:42
- 1.1 Example 2 06:17
- 1.1 Example 3 06:31
- 1.1 Some Notes 04:48
- 1.1 Solving Many Systems 09:22
- 1.2 Reduced Echelon Form 07:00
- 1.2 Examples of Reduced Echelon Form 05:49
- 1.2 Finding Reduced Echelon Form 13:01
- 1.2 Example 1 07:57
- 1.2 Example 2 12:21
- 1.2 Example 3 10:09
- 1.2 Example 4 08:03
- 1.2 Example 5 05:56
- 1.2 Homogeneous Linear System 08:47
- 1.3 Gauss Elimination 33:26
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CHAPTER 2 Matrices
- 2.1 Equal Matrices 05:55
- 2.1 Adding Two Matrices 04:15
- 2.1 Scalar Multiplication of Matrices 05:00
- 2.1 Multiplication of Two Matrices 12:10
- 2.1 Examples of Multiplying Two Matrices 09:00
- 2.1 More Examples of Multiplying Matrices 03:01
- 2.1 Special Matrices 04:52
- 2.1 Properties of Identity Matrix and Zero Matrix 05:08
- 2.1 Partitioning of Matrices 12:18
- 2.2 Algebraic Properties of Matrix Operation 11:34
- 2.2 Number of Multiplications 14:49
- 2.2 Cancellation Law 05:42
- 2.2 Powers of Matrices 08:27
- 2.2 Idempotent and Nilpotent 06:05
- 2.3 Transpose 08:36
- 2.3 Symmetric Matrices 07:03
- 2.3 If and Only If 08:06
- 2.3 Trace of a Matrix 07:48
- 2.3 Matrices With Complex Elements 13:58
- 2.3 Conjugate , Conjugate Transpose, Hermitian 05:48
- 2.4 Inverse of Matrices 08:46
- 2.4 Finding The Inverse 11:35
- 2.4 Properties of Matrix Inverse 10:41
- 2.4 Solving Linear System Using Inverse Matrix 13:13
- 2.4 Elementary Matrix 04:35
- 2.4 Row Operations Using Elementary Matrices 10:10
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CHAPTER 3 Determinants
- 3.1 The Determinant of 2x2 Matrices 06:04
- 3.1 Minor and Cofactor of Elements 09:11
- 3.1 Finding Determinant of Any Square Matrix 10:21
- 3.1 Theorem 3.1 14:48
- 3.1 The Determinant of 3x3 Matrices 04:51
- 3.2 Properties of Determinants Part 1 09:44
- 3.2 Properties of Determinants Part 2 11:20
- 3.2 Properties of Determinants Part 3 11:10
- 3.2 Properties of Determinants Part 4 13:20
- 3.3 Upper and Lower Triangular Matrix 07:21
- 3.3 Evaluating Determinant by Row Operations 12:56
- 3.4 Adjoint Matrix 08:25
- 3.4 Finding Inverse by Adjoint Matrix 09:16
- 3.4 Example of Finding Inverse by Adjoint Matrix 09:58
- 3.4 The Relation Between Determinant and Inverse 04:56
- 3.4 Example of The Relation Between Determinant and Inverse 08:56
- 3.4 The Relation Between Solution of a System and Determinant of Coffeciant Matrix 05:57
- 3.4 Example of The Relation Between Solution of a System and Determinant of Coffeciant Matrix 04:05
- 3.4 Cramer's Rule 07:50
- 3.4 Proof of Cramer's Rule 03:57
- 3.4 Example of Cramer's Rule 04:39
- 3.4 Example 6 07:34
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Exercises of linear algebra
- 1.1 Matrices and System of Linear Equations part 1 (Q1,Q2,Q4,Q5) 09:33
- 1.1 Matrices and System of Linear Equations part 2 (Q6,Q7) 10:20
- 1.1 Matrices and System of Linear Equations part 3 ( Q10(a,b) ) 10:54
- 1.1 Matrices and System of Linear Equations part 4 ( Q10(c) ) 10:21
- 1.1 Matrices and System of Linear Equations part 5 ( Q10(d,e) ) 15:00
- 1.1 Matrices and System of Linear Equations part 6 (Q10(f), Q13) 12:36
- 1.1 Matrices and System of Linear Equations part 7 ( Q11(e) ) 07:04
- 1.1 Matrices and Systems of Linear Equations (Q11(d), !2(a)) 17:10
- 1.2 Gauss Jordan Elimination part 1 ( Q2, Q5(a) ) 14:33
- 1.2 Gauss Jordan Elimination part 2 (Q5(b,c)) 14:28
- 1.2 Gauss Jordan Elimination part 3 (Q5(d,e,f)) 09:19
- 1.2 Gauss Jordan Elimination part 4 (Q8(a)) 11:56
- 1.2 Gauss Jordan Elimination part 5(Q8(b,c,d,e)) 08:34
- 1.2 Gauss Jordan Elimination part 6 (Q8(g,f), Q14(a,b)) 13:46
- 1.2 Gauss Jordan Elimination part 7 (Q1, Q3(a,c,d,e),Q6(f),Q7(d)) 21:20
- 1.2 Gauss-Jordan Elimination (Q6(a,c,e), Q7(c,e)) 39:19
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 1 (Q5) 16:41
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 2 (Q8,Q11,Q17) 15:14
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 3 (Q2, Q4, Q12, Q16) 30:44
- 2.1 Addition, Scalar Multiplication, and Multiplication of Matrices ( Q1(a,b,e,f), Q3(a,b,c,d,h) Q9(b,c,e,g) Q10(a)) 26:22
- 2.2 Properties of Matrix Operations Part 1 (Q6,Q8) 08:46
- 2.2 Properties of Matrix Operations Part 2 (Q19, Q27) 09:54
- 2.2 Properties of Matrix Operations Part 3 (Q31, Q11) 10:13
- 2.2 Properties of Matrix Operations Part 4 (Q3, Q4(a,c), Q5(a), Q12(b,c), Q17, Q24, Q29(a)) 21:41
- 2.2 Properties of Matrix Operations (Q1(a), Q5(c,d), Q30, Q32(c)) 19:18
- 2.3 Symmetric Matrices Part 1 ( Q1(a,d), Q2(a,b,c), Q3(a,b) ) 07:32
- 2.3 Symmetric Matrices Part 2 ( Q5(a,b), Q11, Q23 ) 15:52
- 2.3 Symmetric Matrices Part 3 ( Q1(e,f), Q3(c,e), Q15 ) 09:33
- 2.3 Symmetric Matrices (Q1(i), Q3(d), Q6, Q7, Q14) 17:58
- 2.4 The Inverse of a Matrix Part 1 (Q3(a), Q4(a), 6(a)) 10:10
- 2.4 The Inverse of a Matrix Part 2 (Q6(b,c), Q7(a,b), Q8(a,b)) 14:28
- 2.4 The Inverse of a Matrix Part 3 (Q9(a), Q14, Q15) 10:36
- 2.4 The Inverse of a Matrix Part 4 (Q16, Q19) 07:04
- 2.4 The Inverse of a Matrix Part 5 (Q21) 06:00
- 2.4 The Inverse of a Matrix Part 6 (Q1(b), Q2(b), Q3(b,e), Q4(d), Q5(b), Q7(c), Q9(b), Q18) 52:10
- 2.4 The Inverse of a Matrix (Q1(a,c), Q3(c), Q5(c), Q7(d), Q13, Q17) 30:20
- 3.1 Introduction to Determinants Part 1 (Q1,Q3,Q5) 14:14
- 3.1 Introduction to Determinants Part 2 (Q7) 08:20
- 3.1 Introduction to Determinants Part 3 (Q9) 06:13
- 3.1 Introduction to Determinants Part 4 (Q11, Q13) 15:29
- 3.1 Introduction to Determinant Part 5 (Q6(b), Q8(b), Q14) 22:45
- 3.2 Properties of Determinants Part 1 (Q1) 11:25
- 3.2 Properties of Determinants Part 2 (Q3, Q5, Q7) 12:59
- 3.2 Properties of Determinants Part 3 (Q9, Q13) 10:04
- 3.2 Properties of Determinant ( Q4, Q6(a,b), Q8, Q12(c) ) 17:01
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part1 (Q1, Q5) 11:59
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 2 (Q7) 09:55
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 3 ( Q9, Q11(a) ) 14:13
- 3.3 Determinants, Matrix Inverse and Systems of Linear Equations Part 4 (Q11(b,c), Q13, Q15) 10:27
- 3.3 Determinant, Inverse Matrix, Linear System part 5( Q3(b), Q4(b), Q6(c), Q8(b), Q10(a) ) 20:46
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Exam of Linear algebra
- REVIEW MID 1 01:05:30
- حل ميد 1 عام 2020 جزء 1 16:35
- حل ميد 1 عام 2020 جزء 2 09:59
- حل كويز 1 2020 15:01
- Quiz 1 (عام 2022) 16:14
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CHAPTER 4 Vector Spaces
- 4.1 Introduction to Vectors 04:20
- 4.1 Operation on Vectors 05:10
- 4.1 Examples of Addition and Scalar Multiplication in Vector 07:20
- 4.1 Properties of Rn 06:13
- 4.2 Dot Product 06:56
- 4.2 Norm Vector 04:24
- 4.2 Unit Vector 06:37
- 4.2 The Angle Between Vectors in Rn 05:05
- 4.2 Orthogonal Vectors 09:18
- 4.2 Distance Between Vectors 06:54
- 4.3 Vector Space 20:58
- 4.3 Matrices of Size 2X2 is a Vector Space 08:19
- 4.3 Vector Space of Function 07:26
- 4.3 Useful Properties 04:02
- 4.4 Subspaces 08:30
- 4.4 Examples of Subspace and not Subspace Set 07:08
- 4.4 Vector Space of Polynomial 08:43
- 4.5 Linear Combination 06:58
- 4.5 Is the Vector Linear Combination of Other Vectors ? 06:52
- 4.5 Express Vector as Linear Combination ofSome Vectors 05:10
- 4.5 Liner Combination in Matrices 08:42
- 4.5 Linear Combination in Function 04:33
- 4.5 Spaning Set 11:14
- 4.5 Spanning Set is a Subspace of V 08:37
- 4.5 Equal Spanning Set 09:57
- 4.5 Example 11 04:01
- 4.6 Linearly Dependent and Independent 11:21
- 4.6 More in Linearly Dependent and Independent 07:59
- 4.6 Some Theorems 06:19
- 4.7 Basis 22:19
- 4.7 Some Theorems about Basis 12:11
- 4.7 Dimension 09:16
- 4.7 Some Theorems about Dimension 08:57
- 4.7 True or False 06:49
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CHAPTER 1 System of Linear Equation and Matrices
- math 227 part 1
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