Linear Algebra Playground: Exploring Vectors and Matrices 🧮

Welcome to the Linear Algebra Playground! This tutorial will guide you through the fundamentals of vectors, matrices, and their applications. Let's dive in!

📌 Core Concepts

Vectors

• Definition: A vector is an ordered list of numbers representing magnitude and direction.
• Operations:
  • Addition: A + B
  • Scalar Multiplication: k * A
  • Dot Product: A · B = Σ(a_i * b_i)
• 📝 Example:

  import numpy as np  
  vector = np.array([1, 2, 3])  
  

Matrices

• Definition: A 2D array of numbers arranged in rows and columns.
• Operations:
  • Matrix Multiplication: AB (rows × columns)
  • Determinant: det(A)
  • Inverse: A⁻¹
• 📌 Tip: Use Matrix Calculator for hands-on practice!

🌐 Applications in Real Life

1. Computer Graphics: Transforming 3D objects using matrix operations 🖼️
2. Machine Learning: Representing data and weights in neural networks 🤖
3. Physics: Solving systems of equations in mechanics 🔬

📝 Practice Exercises

Try these examples to reinforce your understanding:

1. Multiply two matrices:

   matrix1 = np.array([[1, 2], [3, 4]])  
   matrix2 = np.array([[5, 6], [7, 8]])  
   result = np.dot(matrix1, matrix2)  
   

2. Calculate the determinant of a 2x2 matrix:

   det = np.linalg.det(matrix1)  
   

📚 Expand Your Knowledge

For deeper insights, explore:

• Eigenvectors and Eigenvalues
• Linear Transformations