Reduced Row Echelon Form

A form of a Matrix, similar to Row Echelon Form but with more restrictions. The RREF of a matrix is always unique .

Definition §

The reduced row echelon form (RREF) must have:

• Already been in Row Echelon Form
• And all leading entries must be 1
• And all columns containing leading entries must otherwise be filled with 0’s

For example:

$$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cccc}1& 0& 3& -3\\ 0& 1& 2& 9\end{array}\right]$$

are all valid RREF matrices

Examples §

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