Reduced Echelon Matrix is Unique
Jump to navigation
Jump to search
Theorem
Every $m \times n$ matrix is row equivalent to exactly one $m \times n$ reduced echelon matrix.
That is, the reduced echelon form of a matrix is unique.
Proof
Proof of Existence
Proved in Matrix is Row Equivalent to Reduced Echelon Matrix.
$\Box$
Proof of Uniqueness
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |