Lec 9 - Echelon Reduce Operations

Monday, January 23, 2012

9:29 AM

- All rows that have at least non-zero entry are above rows with only zeros.
- The leftmost non-zero entry in a row is a 1, called a leading one.
- The leading one in a row is to the right of the leading one in any row above it.
- Any column containing a leading one has it as its only non-zero entry.

Recall:

A matrix is in reduced row echelon form (RREF) if:

(Note: Every Matrix has a UNIQUE RREF)

Eg

Solve

Represents

Solution is:

Eg

Solve

Since there is no choice of variables, this system is inconsistent.

Eg

Solve

Represents:

The solution set of the system is

Definition:

Eg

Solve

Let

The solution set is

Eg

We must solve the system

Homogeneous Systems

Definition

A system of linear equations is homogeneous if the RHS contains only zeros.

Note: Performing ERPs on a homogeneous system will not change the RHS. We just perform EROs on the coefficient matrix.

Eg

Solve

Created by Tim Pei with Microsoft OneNote 2010

One place for all your notes and information