CS223 · Annotated SlidesChapter 2 — LU Factorization
Chapter 2 · Annotated slides

LU Factorization

Factoring A = LU (unit lower triangular L, echelon U), solving Ly = b then Ux = y, and the algorithm that builds L from the row-replacement multipliers.

Slide text Study notes Highlight: key words Tips, tricks & traps Seen again elsewhere How it can come up
Slide 1: Matrix Factorization
Exam weight High
  1. A = LU with L unit lower triangular and U an echelon form of A. Solve Ax = b by Ly = b (forward substitution), then Ux = y (back substitution).
🎯 How this can come up · 1 question
MCQ

After factoring A = LU, solving Ax = b takes:

Slide 2: Example:
Exam weight Low
    Slide 3: An LU Factorization Algorithm
    Exam weight High
    1. Row reduce A to U using only row REPLACEMENTS (adding multiples of rows above); L stores the multipliers with opposite sign below its unit diagonal.
    Memory trickIf R2 → R2 − 3R1, put +3 in L at position (2, 1).