Unit 2 · Vector Spaces and the Four Subspaces

Chapter 2.1

Vector Spaces, Subspaces, and the Nullspace

The subject turns structural: not one solution but the space of all solutions. Ax = 0 defines a subspace — and computing it is elimination again.

12–16 min · in preparation · lesson 4 of 21

By the end

  1. 01Verify subspaces, including column spaces and nullspaces
  2. 02Solve Ax = 0 with special solutions
  3. 03Connect pivot and free variables to the shape of the nullspace

In unit 2

  1. 2.1Vector Spaces, Subspaces, and the Nullspace12–16
  2. 2.2The Complete Solution to Ax = b12–16
  3. 2.3Independence, Basis, and Dimension11–15
  4. 2.4The Four Fundamental Subspaces12–16
  5. 2.5Graphs and Networks11–15
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