REF stands for Reduced Row Echelon Form, a type of matrix used in linear algebra. A matrix is said to be in RREF when it satisfies the following conditions:

1. Leading 1s: In each row that contains non-zero elements, the first non-zero element (called the "leading entry") must be 1.
2. Zero columns above and below leading 1s: The column containing a leading 1 must have all other entries in that column as 0, both above and below the leading 1.
3. Left to right progression: The leading 1 in each row must be to the right of the leading 1 in the row above it.
4. Zero rows at the bottom: Any row that consists entirely of zeros should be at the bottom of the matrix.

Example of a Matrix in RREF:

1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 0 \end{pmatrix}$$ ### Steps to achieve RREF: 1. Identify the leftmost non-zero column (called the "pivot column"). 2. Scale the pivot to 1 by dividing the row by the pivot element. 3. Eliminate all other non-zero elements in the pivot column using row operations. 4. Move to the next pivot column and repeat the process. Would you like to see an example solved, or have questions on a specific matrix? ### Relative Questions: 1. How do you convert a matrix into RREF? 2. What is the difference between row echelon form (REF) and RREF? 3. Can every matrix be transformed into RREF? 4. What are elementary row operations used to compute RREF? 5. How does RREF help in solving systems of linear equations? **Tip**: When transforming a matrix to RREF, always work column by column, and focus on simplifying each pivot and its respective column.