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Gaussian Elimination / Linear Algebra Ladder

Who This Is For

Use this ladder when modular arithmetic basics feel comfortable, but whole linear systems still feel like "too much matrix ceremony."

Warm-Up

  • modular inverse under one prime modulus
  • augmented-matrix notation
  • why row operations preserve the solution set

Core

  • pivot one column at a time
  • normalize the pivot row
  • eliminate the pivot column from all other rows
  • detect free variables versus inconsistency
  • flagship rep: System of Linear Equations

Stretch

  • explain why this route is really "solve over a field"
  • compare prime-mod elimination with xor-basis elimination over GF(2)
  • compare "find any solution" against full affine-solution-space output tasks

Retrieval Layer

Repo Anchors

Exit Criteria

You are ready to move on when you can:

  • explain why one nonzero pivot is enough to own a column
  • say exactly when a variable is free
  • detect 0 = nonzero rows without hesitation
  • explain why the repo starter assumes a prime modulus
  • distinguish this lane from both xor-basis and matrix-exponentiation lanes

External Practice