AlgèbreFacile
Math Learning PlatformLinear Algebra — Vectors and Matrices
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📖 About this lesson
Introduction to vectors, matrices and fundamental operations in linear algebra
Lesson Content
Linear Algebra
Vectors
Quantity with direction and magnitude.
- Addition: (a,b)+(c,d) = (a+c, b+d)
- •Dot product: (a,b)·(c,d) = ac+bd
Matrices
Rectangular array of numbers.
- •Matrix multiplication: (AB)ij = ΣAik·Bkj
Determinant 2×2: det = ad-bcInverse: A⁻¹ = (1det)·adj(A)
Practical Examples
1
Example 1
📋 Problem
Calculer (1,2)·(3,4) (produit scalaire)
✅ Solution
11
💡 Explanation
1×3 + 2×4 = 3 + 8 = 11
2
Example 2
📋 Problem
det([[2,1],[3,4]])
✅ Solution
5
💡 Explanation
det = 2×4 - 1×3 = 8 - 3 = 5
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