Lec 19 - Subspaces and Spanning in a Vector Space

Wednesday, February 15, 2012

9:27 AM

Subspaces

This also happens in other vector spaces.

Definition

Theorem: Subspace Test

Eg

Eg

Eg

Spanning

Definition

Definition

Eg

We get the following system of linear equations:

Put in a matrix: (Drop the 3rd equation)

Eg

We get the following system of linear equations:

The system is inconsistent.

Theorem:

Proof: (by the subspace test)

Created by Tim Pei with Microsoft OneNote 2010

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