Unit 2 · Vector Spaces and the Four Subspaces

Chapter 2.3

Independence, Basis, and Dimension

How big is a space, really? Independence trims the redundancy, a basis is just enough vectors, and dimension is the one number that doesn't depend on your choices.

11–15 min · in preparation · lesson 6 of 21

By the end

  1. 01Test vectors for linear independence
  2. 02Produce bases for column spaces and nullspaces
  3. 03Explain why every basis of a space has the same size

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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