🔮 RREF Calculator
Convert an augmented 3x4 matrix into Reduced Row Echelon Form.
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Use this 3x4 augmented matrix to solve a system of 3 linear equations (x, y, z).
Reduced Row Echelon Form (RREF)
What is Reduced Row Echelon Form (RREF)?
A matrix is in Reduced Row Echelon Form if it satisfies the following conditions:
- All rows containing only zeros are at the bottom of the matrix.
- The leading entry (the first non-zero number from the left) of every non-zero row is a 1.
- The leading 1 of a lower row is always to the right of the leading 1 of a higher row.
- Every column containing a leading 1 has zeros in all its other entries.
In linear algebra, converting an augmented matrix into RREF via Gaussian Elimination is the fastest way to solve a system of linear equations. The final column will directly show you the values of your variables (e.g., x, y, z).
Frequently Asked Questions
What happens if my system has no solution? +
If the system has no solution, the RREF process will result in a row that looks like [0, 0, 0 | 1]. This mathematically means 0 = 1, which is impossible, indicating the system is inconsistent.
What happens if my system has infinite solutions? +
If the system has infinite solutions, the RREF will contain an entire row of zeros [0, 0, 0 | 0], meaning that one of the equations was redundant and the variables are dependent on each other.