Matrices

A matrix is a rectangular array of numbers arranged in rows and columns. Used in linear algebra, computer graphics, engineering, and statistics.

Key Concepts:

1. Types of Matrices:
   • Row, Column, Square, Zero, Identity, Diagonal, Scalar, Symmetric, Skew-symmetric
2. Matrix Operations:
   • Addition, Subtraction, Scalar Multiplication, Transpose
   • Matrix Multiplication: AB = C (number of columns in A = number of rows in B)
3. Determinant & Inverse:
   • Determinant used to check invertibility
   • Inverse A⁻¹ exists if det(A) ≠ 0
4. Applications: Solving linear equations, transformations, network analysis

Example Problem:
A = [[1,2],[3,4]], B = [[5,6],[7,8]]

• A + B = [[6,8],[10,12]]
• AB = [[19,22],[43,50]]

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