Category:Echelon Matrices

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This category contains results about Echelon Matrices.
Definitions specific to this category can be found in Definitions/Echelon Matrices.

Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix.


Echelon Form

$\mathbf A$ is in echelon form if and only if:

$(1): \quad$ The leading coefficient in each non-zero row is $1$
$(2): \quad$ The leading $1$ in any non-zero row occurs to the right of the leading $1$ in any previous row
$(3): \quad$ The non-zero rows appear before any zero rows.


Reduced Echelon Form

The matrix $\mathbf A$ is in reduced echelon form if and only if, in addition to being in echelon form, the leading $1$ in any non-zero row is the only non-zero element in the column in which that $1$ occurs.


Such a matrix is called a reduced echelon matrix.