Phase 0: Linear Algebra Foundations · ~120 minutes · Python

Linear Systems

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

Hiring signal: Understanding of linear systems internals

What you will learn

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

Introduction

Type: Build Language: Python Prerequisites: Phase 1, Lessons 01 (Linear Algebra Intuition), 02 (Vectors & Matrices), 03 (Matrix Transformations) Time: ~120 minutes

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

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build It, Use It, Ship It, Exercises, Key Terms, Further Reading — plus a hands-on lab, quiz, and project artifact.

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