Unit 1 · Solving Linear Systems

Chapter 1.2

Elimination, Matrix Operations, and Inverses

The oldest algorithm in the book, made mechanical: pivots knock out unknowns, elimination matrices record every step, and invertibility is exactly 'elimination succeeds'.

13–16 min · in preparation · lesson 2 of 21

By the end

  1. 01Run elimination with pivots and multipliers, including row exchanges
  2. 02Multiply matrices and express elimination steps as matrix multiplications
  3. 03Compute inverses with Gauss-Jordan and characterize when A⁻¹ exists

In unit 1

  1. 1.1The Geometry of Linear Equations11–15
  2. 1.2Elimination, Matrix Operations, and Inverses13–16
  3. 1.3LU Factorization, Transposes, and Permutations12–16
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