Algèbre 2 —
Vector Spaces, Linear Maps, Matrices, Change of Bases, and Linear Systems
Teacher : Pr.Nasreddine
جميع الفيديوهات مشروحة باللغة العربية بأسلوب مبسّط وواضح لفهم التطبيقات الخطية بسهولة.
Chaptre 01 : Vector space
V1.2 | How to Check if a Set is a Subspace (Step-by-Step)
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V1.3 | Subspace or Not? Don’t Get It Wrong!
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V1.4 | Don’t Miss This! Subspaces of Polynomial Spaces Made Easy.
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V1.5 | Master Matrix Subspaces in Minutes
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V1.6 | 3 Powerful Methods to Check Linear Independence.
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V1.7 | Linear Independence with Parameters (Step-by-Step). HIS 2026.
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V1.8 | Linear Independence of Polynomials.
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V1.9 | Find the Intersection of Vector Spaces (Full Method)
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V1.10 | Find the Sum of Subspaces Step-by-Step.
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V1.11 | Supplementary Subspaces Simply Explained
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Chaptre 02 : Linear Maps
1. Linear Maps Basics
V1.2 | Recall Essential | Key concepts for Linear Maps Part 01
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V1.3 | Key Sets and Structures | Essential mathematical structures you must know.
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2. Kernel, Image and Rank
V2.1 | Checking Linearity: Methods to verify if a map is linear.
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V2.2 | Kernel of Linear Maps: Finding and understanding ker(f).
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V2.3 | Rank-Nullity Theorem: Using the relation dim(V) = rank(f) + nullity(f).
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V2.4 | Image of Linear Maps. First Method: Determining the subspace Im(f).
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V2.5 | Image of Linear Maps: Second Method
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3. Exercises
V3.1 | Exercise 01 | ENSIA 2026.
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V3.2 | Exercise 02 | ENSIA 2026.2.
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V3.3 | Exercise 03 | University of Nice Sophia Antipolis.
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V3.4 | Exercise 04 | University of Blida 01.
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4. Tests and Exams
V4.1 | Test 01 - USTHB 2025.
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V4.2 | Test 02 - Computer Science | USTHB 2025.
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V4.3 | Test 03 - USTHB 2025.
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V4.4 | Test 04 - Mathematics Track.
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V5.1 | Exam 01 - (09 pts) USTHB 2025.
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V5.2 | Exam 02 - Computer Science Exam - USTHB 2023.
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V5.3 | Exam 03 Resit Exam - USTHB 2025.
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V5.4 | Exam 04 General Exam - USTHB.
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V5.5 | Exam - Boumerdes.
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Chaptre 03 : Matrices (Les matrices)
1. Matrix Basics
V1.2 | Sum and Difference | Adding and subtracting matrices entry-wise.
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V1.3 | Scalar Multiplication — Multiplying a matrix by a scalar.
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V1.4 | Matrix Multiplication — Product of two matrices and main properties.
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V1.5 | Matrix Transpose — Interchanging rows and columns.
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V1.6 | Trace of a Matrix — Sum of diagonal elements.
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2. Advanced Matrix Tools
V1.7 | Matrix Row Reduction — Transforming matrices into echelon form.
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V1.8 | Matrix Power — Computing powers of matrices.
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V1.9 | Matrix Power — Second example — Computing powers of matrices.
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V1.10 | Matrix power -- Correction Test USTHB 2026.
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3. Determinants
V2.1 | Determinant of a 2x2 Matrix.
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V2.2 | Determinant of 3x3 Matrix.
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V2.3 | Determinant 3x3 Matrix — Exercise.
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V2.4 | Sarrus Method — Determinant 3x3 Matrix.
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4. Matrix Inverse
V3.1 | The Cofactor Method. First Method for Determining the Inverse of a Matrix.
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V3.2 | The Gaussian Elimination Method: Second Method for Determining the Inverse of a Matrix.
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V3.3 | The Annihilating Polynomial Method: Third Method for Determining the Inverse of a Matrix.
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5. Matrix Exercises and Tests
V4.1 | Exercise 1_ENSIA: Matrix Operations.
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V4.2 | Exercise 2_USTHB. Matrix Operations.
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V4.3 | Exercise 3_USTHB: Matrix Operations.
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V5.1 | Test 01 USTHB. Full correction.
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6. Change of basis
V6.1 | USTHB 2026 Test 2 Correction | Change of Basis: Matrix Representation.
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V6.2 | The Passage Matrix | USTHB 2026 Test 3 Correction | Change of Basis: Matrix Representation.
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Chaptre 04 : Linear Systems
1. Linear Systems Methods
V1.2 | Solve Linear Systems using Gaussian Elimination | Method 1 (Step-by-Step).
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V1.3 | Solve Linear Systems using Cramer’s Rule | Method 2 (Step-by-Step).
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V1.4 | Solve Linear Systems using the Inverse Matrix Method | Method 3 (Step-by-Step).
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2. Linear Systems with Parameters
V2.1 | Solve Linear Systems with Real Parameters (Step-by-Step Guide).
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3. Exams and Full Corrections
V3.1 | Exam 1: Linear Systems with Parameters (Full Correction).
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V3.2 | Exam 2: Matrix & Linear Systems with Parameters (Full Correction).
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