Unit 2 · Vector Spaces and the Four Subspaces

Chapter 2.2

The Complete Solution to Ax = b

Rectangular systems drop the safety net: solutions may not exist, or may come in families. One particular solution plus the whole nullspace is every answer there is.

12–16 min · lesson 5 of 21

By the end

  1. 01Reduce rectangular matrices to row reduced echelon form R
  2. 02Decide solvability and write the complete solution x = x_p + x_n
  3. 03Read rank and its consequences from R

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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