الجبر الخطي ريض 244
Matrices and their operations. Types of matrices. Elementary transformations. Linear systems of equations. Determinants, elementary properties. Inverse of a matrix. Vector spaces, linear independence,
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Introduction
- introduction 06:18
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CHAPTER 1 System of Linear Equation and Matrices
- 1.1 Linear Equation 12:45
- 1.1 Solution of System of Linear Equations 10:25
- 1.1 Number of Solution 14:17
- 1.1 Solving The System of Linear Equation 08:53
- 1.1 Solving The System of Linear Equation (infintly many solution) 13:02
- 1.1 Augmented Matrices and Elementary Row Operations 08:31
- 1.1 Using Elementary Row Operations 20:45
- 1.2 What We Are Going To Do? 05:19
- 1.2 Echelon Form 10:00
- 1.2 Examples for Echelon Form 06:26
- 1.2 Solution from Echelon Form Part1 03:08
- 1.2 Solution from Echelon Form Part2 09:57
- 1.2 Gauss and Gauss Jordan Methods 18:24
- 1.2 Solve By Gauss 13:54
- 1.2 Solve By Gauss Jordan 09:38
- 1.2 Example 5 18:34
- 1.2 Homogeneous Linear System 05:50
- 1.2 Solving Homogeneous Linear System 03:51
- 1.2 Free Variable Theorem 05:52
- 1.2 Back Substitution 06:02
- 1.2 Example 8 03:42
- 1.2 Some Fact About Echelon Form 05:00
- 1.3 Introduction to Matrices 06:34
- 1.3 More About Matrices 07:11
- 1.3 Equal Matrices 03:20
- 1.3 Adding Two Matrices 05:29
- 1.3 Scalar Multiple 05:08
- 1.3 Multiplying Two Matrices 11:46
- 1.3 Examples of Multiplying Two Matrices 07:32
- 1.3 Matrix Multiplication by Columns and by Rows 06:48
- 1.3 Example 7 04:32
- 1.3 Linear Combinations of Matrices 03:31
- 1.3 Theorem 1.3.1 05:12
- 1.3 Example 9 03:08
- 1.3 Columns-Rows Expansion 06:16
- 1.3 Matrix Form of a Linear System 02:20
- 1.3 Transpose of a Matrix 04:38
- 1.3 Trace of a Matrix 03:09
- 1.4 Properties of Matrices 07:50
- 1.4 Properties of Matrix Multiplication 05:37
- 1.4 Zero Matrix and It's Properties 04:34
- 1.4 Cancellation Law and Zero Product in Matrices 05:28
- 1.4 Identity Matrix 06:47
- 1.4 Theorem 1.4.3 02:24
- 1.4 Inverse of a Matrix 09:16
- 1.4 Uniqueness of Inverse 05:06
- 1.4 Finding The Inverse of 2x2 Matrices 08:47
- 1.4 Example 7 03:19
- 1.4 Example 8 02:23
- 1.4 Product of Invertible Matrices 06:38
- 1.4 Powers of a Matrix Part 1 06:14
- 1.4 Powers of a Matrix Part 2 06:45
- 1.4 Matrix Polynomial 03:42
- 1.4 Properties of Transpose 08:02
- 1.5 Inverse Row Operation 07:52
- 1.5 Elementary Matrix 06:07
- 1.5 Row Operation by Matrix Multiplication 08:22
- 1.5 Inverse Operations in Elementary Matrix 07:26
- 1.5 Equivalent Statement 06:47
- 1.5 Using Row Operations to Find the Inverse 09:12
- 1.5 Showing That a Matrix Is Not Invertible 04:45
- 1.6 Solving Linear System By Inverse of Matrix 08:21
- 1.6 Solving Many Linear System at Once 08:33
- 1.6 More Properties of Invertible Matrices 03:47
- 6.1 Determining Consistency 12:09
- 1.7 Diagonal Matrix 11:07
- 1.7 Triangular Matrix 08:58
- 1.7 Symmetric Matrices 10:50
- 1.7 Product of a Matrix With its Transpose 09:03
- 1.8 Matrix Transformation 12:46
- 1.8 Standard Matrix 15:21
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CHAPTER 2 Determinants
- 2.1 Minors And Cofactors 17:16
- 2.1 Definition of a General Determinant 10:09
- 2.1 Smart Choice of Row and Column 09:03
- 2.1 Determinant of Triangular Matrix 04:58
- 2.1 Evaluating of 3X3 Determinants 05:04
- 2.2 Basic Theorems 03:02
- 2.2 Elementary Row Operations 09:09
- 2.2 Determinant of Elementary Matrices 06:49
- 2.2 Matrices with Proportional Rows or Columns 05:46
- 2.2 Evaluating Determinant by Row Reduction 04:54
- 2.2 Extra Examples 04:38
- 2.2 Another Ways to Evaluate Determinant 09:06
- 2.3 determinant KA 05:26
- 2.3 det(A+B) 07:10
- 2.3 det(AB) 02:42
- 2.3 Determinant Test for Invertibilty 06:01
- 2.3 Entries and Cofactor From Different Rows 05:56
- 2.3 Adjoint Matrix 08:11
- 2.3 Using the Ajoint to Find an Inverse Matrix 03:56
- 2.3 Cramer's Rule 09:28
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CHAPTER 3 Euclidean Vector Spaces
- 3.1 Introduction to Victors 04:44
- 3.1 Operations on Vectors 09:05
- 3.1 Vectors in Coordinate Systems 08:44
- 3.1 n-Space 09:52
- 3.1 Linear Combinations 05:39
- 3.2 Norm of a Vector 07:06
- 3.2 Unit Vector 05:14
- 3.2 Standard Unit Vectors 12:11
- 3.2 Distance in n-Space 04:42
- 3.2 Dot Product Part 1 09:20
- 3.2 Dot Product Part 2 04:21
- 3.2 Algebraic Properties for Dot Product 06:26
- 3.2 Cauch - Schwarz Inequality 05:43
- 3.2 Parallelogram Equation for a Vector 05:20
- 3.2 Dot Product as Matrix Multiplication 07:18
- 3.2 Example 9 08:21
- 3.3 Orthogonality 07:10
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CHAPTER 4 General Vector Spaces
- 4.1 Vector Space 08:43
- 4.1 Examples of Vector Space 10:44
- 4.1 More Examples of Vector Space 07:58
- 4.1 The Vector Space of Real Valued Function 09:49
- 4.1 A Set that is Not a Vector Space 04:30
- 4.1 An Unusual Vector Space 12:12
- 4.1 Exercise 11 11:02
- 4.1 Extra Example of a Set that is Not a Vector Space 08:38
- 4.2 The Meaning of subspace 07:25
- 4.2 Subspaces of R2 10:10
- 4.2 Subspaces of R3 and Mnn 09:26
- 4.2 Subspaces of Funations 09:12
- 4.2 Linear Combination 06:31
- 4.2 Example ( Is w a linear combination of Other Vectors ? ) 11:57
- 4.2 Spanning Set 11:55
- 4.2 Testing for Spanning 12:19
- 4.2 Equal Spanning Sets 04:26
- 4.2 The Solution of a Homogeneous linear System 04:05
- 4.2 Solution Spaces of Homogeneous Linear System 07:20
- 4.2 Matrix Transformation 03:35
- 4.3 Linearly independence 22:18
- 4.3 Linearly Independent of Polynomials 13:32
- 4.3 Wronskian 14:49
- 4.4 Basis 13:27
- 4.4 Uniqueness of Basis Representation 06:51
- 4.4 Coordinates 09:29
- 4.5 Dimension 09:53
- 4.5 Plus Minus Theorem 26:05
- 4.6 Change of Basis (Basic Idea) 18:34
- 4.6 Finding Transition Matrix and Computing coordinates vectors (Example 1 and 2) 18:52
- 4.6 Invertibility of Transition Matrix - Learning New Procedure to Compute Transition Matrix 10:52
- 4.7 Row Space, Vector Space, Null Space 07:56
- 4.7 The Relationship Between Ax=b and col(A) and null(A) 16:03
- 4.7 Basis of null(A) 08:46
- 4.7 Basis for row(A) and Col(A) 10:38
- 4.7 Basis for the Space Spanned by a Set of Vectors 14:53
- 4.7 summarize 05:14
- 4.8 Rank and nullity 08:52
- 4.8 Some Theorems about Rank and nullity 11:30
- 4.8 The fundamental spaces of a Matrix 07:19
- 1.8 Matrix Transformation 12:46
- 1.8 Standard Matrix 15:21
- 4.8 Overdetermind and underdetermind 12:32
- 4.9 Reflection Operator 13:28
- 4.9 Projection Operator 15:50
- 4.9 Dilation and Contraction 08:34
- 4.10 Composition of Matrix Transformation 09:13
- 4.10 Examples of Composition 19:41
- 4.10 One-to-one Matrix Transformation 07:03
- 4.10 Kernel and Range 10:40
- 4.10 Inverse Operator 09:59
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CHAPTER 5 Eigenvalues and Eigenvectors
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CHAPTER 6 Inner Product Space
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CHAPTER 8 General Linear Transformation
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Exercises
- 1.1 Introduction to Systems of Linear Equations part1 09:53
- 1.1 Introduction to Systems of Linear Equations part2 13:06
- 1.1 Introduction to Systems of Linear Equations part3 10:34
- 1.1 Introduction to Systems of Linear Equations part4 15:48
- 1.2 Gaussian Elimination part 1 09:45
- 1.2 Gaussian Elimination part 2 07:40
- 1.2 Gaussian Elimination part 3 05:14
- 1.2 Gaussian Elimination part 4 10:30
- 1.2 Gaussian Elimination part 5 10:41
- 1.2 Gaussian Elimination part 6 08:49
- 1.2 Gaussian Elimination part 7 11:25
- 1.2 Gaussian Elimination part 8 13:03
- 1.3 Matrices and Matrix Operations Part 1 08:43
- 1.3 Matrices and Matrix Operations Part 2 08:33
- 1.3 Matrices and Matrix Operations Part 3 12:34
- 1.3 Matrices and Matrix Operations Part 4 12:51
- 1.3 Matrices and Matrix Operations Part 5 08:50
- 1.4 Inverses;Algebraic Properties of Matrices Part 1 08:35
- 1.4 Inverses;Algebraic Properties of Matrices Part 2 13:17
- 1.4 Inverses;Algebraic Properties of Matrices Part 3 13:44
- 1.5 Elementary Matrices and a Method for Finding the Inverse Part 1 11:28
- 1.5 Elementary Matrices and a Method for Finding the Inverse Part 2 19:14
- 1.5 Elementary Matrices and a Method for Finding the Inverse Part 3 17:12
- 1.6 More on Linear Systems and Invertible Matrices Part 1 10:36
- 1.6 More on Linear Systems and Invertible Matrices Part 2 10:58
- 1.6 More on Linear Systems and Invertible Matrices Part 3 16:55
- 1.7 Diagonal, Triangular, Symmetric Matrices 30:19
- 1.8 Matrix Transformations 21:12
- 2.1 Determinants by Cofactor Expansion Part 1 13:28
- 2.1 Determinants by Cofactor Expansion Part2 17:55
- 2.1 Addition, Scalar Multiplication, Multiplication of Matrices Part 3 15:33
- 2.2 Evaluating Determinant by Row Reduction Part 1 07:30
- 2.2 Evaluating Determinant by Row Reduction Part 2 10:28
- 2.2 Evaluating Determinant by Row Reduction Part 3 12:32
- 2.3 Properties of Determinant, Cramer's Rule Part 1 12:22
- 2.3 Properties of Determinant, Cramer's Rule Part 2 16:05
- 2.3 Properties of Determinant, Cramer's Rule Part 3 07:30
- 2.3 Properties of Determinant, Cramer's Rule Part 4 06:50
- 3.1 Vectors in 2-Space, 3-Space and n-Space Part 1 11:42
- 3.1 Vectors in 2-Space, 3-Space and n-Space Part 2 07:12
- 3.2 Norm, Dot Product and distance in n-Space Part 1 12:10
- 3.2 Norm, Dot Product and distance in n-Space Part 2 13:52
- 3.3 Orthogonality Part 1 07:33
- 3.3 Orthogonality Part 2 08:49
- 4.1 Real Vector Spaces Part 1 18:48
- 4.1 Real Vector Spaces Part 2 15:44
- 4.1 Real Vector Spaces Part 3 23:15
- 4.2 Subspaces Part 1 24:22
- 4.2 Subspaces Part 2 17:06
- 4.2 Subspaces Part 3 24:50
- 4.3 Linear Independence Part 1 24:24
- 4.3 Linear Independence Part 2 22:30
- 4.4 Coordinates and Basis Part 1 18:08
- 4.4 Coordinates and Basis Part 2 09:59
- 4.5 Dimension 19:36
- 4.6 Change of Basis 18:54
- 4.7 Row Space, Vector Space, Null Space 26:22
- 4.8 Rank, Nullity and the Fundamental Matrix Spaces 24:30
- 4.9 Basic Matrix Transformation 15:19
- 4.10 Properties of Matrix Transformation Part 1 26:13
- 4.10 Properties of Matrix Transformation Part 2 15:36
- 5.1 Eigenvalue and Eigenvectors Part 1 16:12
- 5.1 Eigenvalue and Eigenvectors Part 2 15:32
- 5.2 Diagonalization 45:45
- 6.1 Inner Products 01:07:58
- 6.2 Angle and Orthogonality in Inner Product Spaces 29:16
- 6.3 Gram–Schmidt Process; QR-Decomposition 37:19
- 8.1 General Linear Transformation 01:15:35
- 8.4 Matrices for General Linear Transformations 01:06:40
- Tutorials
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حل أسئلة سابقة
- حل أسئلة سابقة 1 (mid 1) 22:50
- حل أسئلة سابقة 2 (mid 1) 17:01
- أسئلة سابقة 3 (mid 1) 55:09
- حل أسئله سابقه 4 (mid 1) 01:09:00
- 5 Mid 1 - girls - 1443 - 2022 53:26
- 6- Mid 1 - 2023 - term 1 01:32:47
- Quiz 1 (عام 2022) 29:22
- Quiz 1 (Boys) 28:42
- Final 5 ( 1444 عام ) - فقط حل الأسئله الاختياريه و الصح و الخطأ 33:25
- Final 5 ( 1444 عام ) - السؤال 2 و 3 39:42
- Final 5 ( 1444 عام ) -a السؤال الخامس فقره 20:55
- Quiz 1 (2021) 29:11
- Final 1 54:33
- Final 2 ( عام 2020 ) 01:09:51
- Final 3 (نموذج بعد التحديث) 41:59
- Final 4 - 2021 (boys and girls) 01:12:16
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Homework
- Homework 1 09:33
- Homework 3 10:16
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Five Questions Tutorial
- 5 Questions (ch1) 11:36
- 5 Questions (ch2) 15:37
- 5 Questions (ch3) 13:44
- 5 Questions (ch4) 19:24
- 5 Questions (ch4) part 2 12:58
- 5 Questions (ch4) and (ch3) 12:37
- 5 Questions (ch4) and (ch3) part2 09:09
- 5 Questions (ch4) part 3 14:02
- 5 Questions (ch5) 13:23
- Five Questions 10 (ch1)
- Five Questions 11 (ch4) part 4 11:01
- Five Questions 12 (ch4 and ch5) 13:40
- Five Questions 13 (ch4) part 5 28:30
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سؤال و جواب
- ِQ1 : (about quiz 1) 10:57
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Introduction
- Matrices and their operations. Types of matrices. Elementary transformations. Linear systems of equations. Determinants, elementary properties. Inverse of a matrix. Vector spaces, linear independence, finite dimensional spaces, linear subspaces. Linear transformations, kernel and image of a linear transformation. Eigenvalues and Eigenvectors of a matrix and of a linear operator
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• Hadeel Mohammed Almadiny. • Lecturer in Vision Academy. • Specialty in mathematics. • Graduated from (KSU)with calss honor. ~ Experiences: • teacher in international school. • English language. • Strategic teaching course. ~ Achievements: • Title of scientific meeting leader in KSU.
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التقسيط متاح
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شرح بسيط وتوصل المعلومه بسرعه 💕
مبدعه توصل الشرح بطريقه ممتعه وواضحة
شرح واضح وملم ، تثبت المعلومة ومايضيع وقتك ✅
شرح جميل مرة
توصل لك المعلومة بأفضل واسرع طريقة ممكنه✔️
شرح واضح وبسيط ، وتوصل المعلومة بسرعه
تشرح من كل قلب وتوصل المعلومة بشكل يسير وجدا متعاونة ، الله يوفقها يارب ويسعدها
كانت المادة مع مس هديل مرة واااضحة وسهلة وبسيطة والله يسعدها كانت كثير متعاونة + كنت افضل أن مدة المقاطع تكون اطول شوية لان مدتها قصيرة جدًا بالنسبة لي لكن الشرح ما يشوبه شائبة ، الله يسعدها❤️
❤️❤️مرره حلو شرحها
الشرح ممتاز وبسيط ومختصر وينفهم وما يطفّش 👍🏼👍🏼
اولا اشكر الله ثم اشكر المنصه الرائعة جدا مريحه فالتعامل ومرتبه واشكر تيتشر هديل اللي فعلاً انقذتني من الفوضى مع هالماده على انها سهله الا انها تحتاج تركيز خصوصا عشانه عن بعد حرفيا كنت معتمده على شرح تيتشر هديل ولا ادري عن شرح تيتشرت الجامعه وحمدلله احس اني افضل حال من اللي يعتمدون على شرح الاستاذه وصدقا ماكنت اذاكر اول باول لكن شرح استاذه هديل فعلا. بسيط لدرجة انه كان يمدي اجمع بفضل الله اولا طبعا . والشي اللي اعجبني تعاون استاذه هديل معنا بقروب التيليقرام و ان المقاطع بسيطه وسهله و انها تحلّ التمارين كلها يعني اللي بيشترك ماراح يخسر ولا شي والله يوفقك يارب استاذه هديل وان شاء الله اذا فيه ماده اقدر اخذها معك ماراح اتردد 💜
استاذة هديل من الشروحات الرائعة جدًا توصلك المعلومة و تفهمين المفاهيم معها ،، و متعاونة جدًا مع الطالبات كورس ممتاز لاصحاب هذي الماده تغنيك عن اي مراجعاخرى
شرح مبسط وواضح شكرًا لك
اولاً اشكر أ.هديل على شرح المقرر بصورة مبسطة وواضحة جداااً والله يجعله يارب من موازين حسناتك . بنات الي متردد انه يشترك لاتفكر اصلا وين بتلقى مثل كيذا استاذة قمة في الشرح اعطيها 10/10 مبدعه في ايصال المعلومة وهذا غير تعاملها معانا بالتلجرام اذا كان عندنا اي سؤال نسأله فعلياً ماقصرررت معانا اببد واكرر مره ثانيه اذا كنتي مترددة سجلي وانتي مغمضة وبس
شرح مختصر وتوصل المعلومة بسرعة تبارك الله ما ندمت ولا للحظة اني اشتركت
الكورس ممتاز جدا وندمت اني ما اشتركت من بداية الترم شرح كافي ووافي ججدا والمميز انه بسيط ومختصر بشكل يخليك تنجز في فترة وجيزة بفهم عالي بالاضافة الى تعاون الاستاذه في مجموعة التيليجرام وردها على جميع الاستفسارات أول بأول أنصح بالاشتراك معها وبقوة
Ms. Hadeel was very helpful and cooperative with all of us. She made the subject easy and simple. and most important , she always responds to every question I ask !
رائعة ومميزة