Is the echelon form of a matrix unique?
Understand the Problem
The question is inquiring about the uniqueness of the echelon form of a matrix, specifically whether a given matrix can have multiple echelon forms or if there is only one standard form.
Answer
False
False. The reduced echelon form is unique.
Answer for screen readers
False. The reduced echelon form is unique.
More Information
The reduced row-echelon form (RREF) of a matrix is unique, which is not the case for the general row echelon form (REF). The same matrix can have multiple row echelon forms depending on the sequence of row operations.
Tips
A common mistake is to confuse row echelon form (REF) with reduced row echelon form (RREF). Remember that only the RREF is unique.
Sources
- Is the row echelon form of a system of equations unique? - math.stackexchange.com
- 1.4: Uniqueness of the Reduced Row-Echelon Form - math.libretexts.org
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