1. What is Reduced Row Echelon Form (RREF)?

RREF is a simplified form of a matrix achieved through Gaussian elimination. A matrix is in RREF when it satisfies these conditions:

1. All zero rows are at the bottom
2. The leading coefficient (first non-zero number) of each non-zero row is 1 (called a leading 1)
3. Each leading 1 is the only non-zero entry in its column
4. The leading 1 of each row is to the right of the leading 1 in the row above

2. How Does Gaussian Elimination Work?

The process involves three elementary row operations:

Algorithm Steps:

• Forward Elimination: Create zeros below each pivot
• Back Substitution: Create zeros above each pivot
• Normalization: Make each pivot equal to 1

3. Importance of RREF

Applications: Solving systems of linear equations, finding matrix rank, determining linear independence of vectors, matrix inversion, and more.

4. Using the Calculator

Instructions: Enter your matrix with rows separated by semicolons (;) and columns separated by commas. Example: "1,2,3;4,5,6" creates a 2×3 matrix.

5. Frequently Asked Questions (FAQ)

Q1: What if my matrix has inconsistent rows?
A: The calculator will still produce RREF, which may help identify inconsistent systems (rows like [0 0 ... 0|1]).

Q2: Can I use fractions or decimals?
A: Use decimal numbers only. The calculator will display results with 4 decimal places.

Q3: What's the maximum matrix size?
A: There's no hard limit, but very large matrices may cause performance issues.

Q4: How accurate are the results?
A: Results are accurate to floating-point precision. For exact fractions, use symbolic computation software.

Q5: Can I copy/paste matrices from Excel?
A: Yes, copy tab-separated values from Excel and replace tabs with commas and newlines with semicolons.