# Solving Linear Equations

## Row Echelon Form

* All nonzero rows are above any rows of all zeros. 
* Each leading entry (i.e. left most nonzero entry) of a row is in a column to the right of the leading entry of the row above it. 
* All entries in a column below a leading entry are zero.

<figure><img src="/files/MO9v7SGwKSgI1hsBErUQ" alt=""><figcaption></figcaption></figure>

## Reduced Row Echelon Form

Add the following conditions to conditions 1, 2, and 3 above:

* The leading entry in each nonzero row is 1.&#x20;
* Each leading 1 is the only nonzero entry in its column


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