LU Decomposition Result:
Lower Triangular Matrix (L):
Upper Triangular Matrix (U):
Steps to Perform LU Decomposition:
- Start with a square matrix (A) (n x n).
- Initialize an identity matrix (L) for the lower triangular matrix and a zero matrix (U) for the upper triangular matrix.
- For each pivot element in matrix (A), apply Gaussian elimination to eliminate the elements below the pivot, updating (L) and (U) accordingly.
- The diagonal elements of (U) remain as pivots, and (L) contains the multipliers used during elimination.
- Resulting matrices satisfy ( A = L * U ) .