Sign inStart free
AI Engineering/Phase 01/Lesson 17

Linear Systems

Solving Ax = b is the oldest problem in mathematics that still runs your neural network.

Build 2 hr Python

Prerequisites: Phase 1, Lessons 01 (Linear Algebra Intuition), 02 (Vectors & Matrices), 03 (Matrix Transformations)

#Learning Objectives

  • Solve Ax = b using Gaussian elimination with partial pivoting and back substitution
  • Factor matrices with LU, QR, and Cholesky decompositions and explain when each is appropriate
  • Derive the normal equations for least squares and connect them to linear and ridge regression
  • Diagnose ill-conditioned systems using the condition number and apply regularization to stabilize them
Full Access lesson

Keep going. The rest of this lesson is one step away.

Unlock all 503 lessons, video, code, quizzes and every future update. Pay in your own currency with Paystack.

See plans Sign in

The text and code of this lesson are based on AI Engineering from Scratch by Rohit Ghumare, MIT licensed.