Paste your matrix using spaces and new lines (e.g. "1 2 3\n4 5 6\n7 8 9") and get the Reduced Row Echelon Form instantly.
What is RREF?
RREF stands for Reduced Row Echelon Form. It’s a form of a matrix where each leading entry is 1, and all values above and below leading 1s are zero. It’s used to solve systems of linear equations efficiently.
How do I input my matrix?
Enter each row on a new line, and use spaces to separate values. Example:
1 2 3\n4 5 6\n7 8 9
When do you use RREF?
In linear algebra, RREF is used for:
Does every matrix have a unique RREF?
Yes — every matrix has one unique reduced row echelon form. This makes it especially useful in proofs and solving equations consistently.
Can I see the row operations used?
Currently this tool shows the final RREF only, but we plan to add a step-by-step breakdown soon.
What’s an example of RREF?
For matrix:
1 2 -1 3 2 4 1 7 -1 2 5 1The RREF is:
1 0 0 2 0 1 0 -1 0 0 1 3
Can you explain RREF like I’m in 5th grade?
Sure! Imagine you’re cleaning up a messy row of boxes so it’s neat and in order. You want each row to start with a “1 box,” and all the boxes above and below that spot must be empty (like 0). That way, it’s super easy to figure out what each row means. RREF is just a fancy way to make a math table super clean, so you can solve problems without getting confused. It’s like organizing your math homework into perfect rows!
What is a pivot in RREF?
A pivot is the first non-zero number in a row (usually a 1). In RREF, every pivot is a 1, and it must be the only non-zero number in its column.
How do I know my matrix is in RREF?
Check three things: (1) each leading number is 1, (2) the pivot 1s move to the right as you go down, and (3) everything above and below a pivot is 0.
Is RREF used outside of math class?
Yes! Engineers, economists, computer scientists, and physicists all use RREF to solve systems or work with data that behaves like a system of equations.
Why are there so many zeroes in RREF?
Zeroes help isolate each variable. RREF simplifies the system so each variable appears once in its own equation without being mixed with others.
Can I use RREF to check my homework?
Absolutely. Enter the matrix from your textbook or worksheet and see if your steps match. Use this to spot errors and build confidence.
How is RREF different from REF?
REF (Row Echelon Form) only requires that all non-zero rows are above zero rows and pivot positions go down and right. RREF takes this further by requiring each pivot to be 1 and all other values in the pivot column to be 0.