LU Decomposition Simplified: Matrix Breakdown For Efficient Solutions

LU decomposition is a fundamental technique in linear algebra that simplifies solving systems of linear equations, computing matrix inverses, and calculating determinants. It breaks down a square matrix into two simpler triangular matrices: one lower triangular (L) and one upper triangular (U). This makes solving complex problems computationally efficient and straightforward.


  
  
  What is LU Decomposition?

LU decomposition expresses a square matrix A as the product of two matrices:

L: A lower triangular matrix with 1s on the diagonal.
U: An upper triangular matrix.

Mathematically:

A =...