Definition of reduced row echelon form of a matrix

**Definition:** The **reduced row echelon form** of a matrix $A$ is the **unique** matrix $R$ in RREF that is row-equivalent to $A$.

**Uniqueness Theorem:** Every matrix is row-equivalent to exactly one matrix in reduced row echelon form.

**Why this matters:** The RREF is a canonical form — it provides a unique "fingerprint" for the row space of a matrix. For matrices of the same shape, having the same row space is equivalent to having the same RREF.

**Computation:** The RREF is found by applying Gauss-Jordan elimination: forward elimination to reach REF, then scaling pivots to 1, then backward elimination to clear entries above pivots.Copy