Lec 22 - Dimensions

Wednesday, February 29, 2012

9:30 AM

- A minimal spanning set of the vector space
- A maximal linearly independent set of the vector space.

We can interpret a basis as:

Definition

Eg

Eg

Theorem:

Proof of 3:

Q.E.D.

Theorem:

Proof: A7

Eg

Eg

This gives a system of linear equations:

Row reduce the coefficient matrix:

Since rank of coefficient matrix equals the # of columns and the system Is consistent, the system has a unique solution.

Coordinates

But we could also use another basis.

Eg

Definition

Note: Order of basis vectors matters.

Eg

Eg

Created by Tim Pei with Microsoft OneNote 2010

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