Lec 9 - Echelon Reduce Operations

Monday, January 23, 2012

9:29 AM

Recall:

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

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

(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

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