A matrix is in echelon form when:
1) Each row containing a non-zero number has the
number “1” appearing in the row’s first non-zero column.
(Such an entry will be referred to as a “leading one”.)
2) The column numbers of the columns containing the first
non-zero entries in each of the rows strictly increases from
the first row to the last row. (Each leading one is to
the
right
of any leading one above it.)
3) Any row which contains all zeros is below the rows
which contain a non-zero entry.
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
The three conditions above will ensure that the entries
below the leading ones
(in each row which contains a non-
zero entry) are
all zeros
.
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A matrix is in reduced echelon form when:
in addition to the three conditions for a matrix to be in
echelon form,
the entries
above the leading ones
(in each row which
contains a non-zero entry)
are all zero’s
.
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Note that if a matrix is in Reduced Row Echelon Form
then it must also be in Echelon form.
