Reduced Row Echelon Form

Reduced row echelon form (rref) is a handy form to solve linear transformations and other systems of equations. It reduces the number of variables (represented by the number of columns) in each equation (represented by the rows) to as few as possible. It also makes the first variable in each equation have a coefficient of just one.

To be in rref, a matrix must satisfy the following properties:

1. Leading One: the first non-zero entry in every row must be a one
2. Upper Triangle: leading ones on a row farther down must be farther right than the leading one above it.
3. All Alone: For every leading one, every other entry in the column must be zero

You can get a matrix into rref by performing row operations

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