A matrix is in
echelon form
when:
1) Each row containing a nonzero number has the
number “1” appearing in the row
’
s first nonzero column.
(Such an entry will be referred to as a “leading one”.)
2) The column numbers of the columns containing the first
nonzero 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 nonzero 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
.
______________________________________________
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 nonzero entry)
are
all zero
’
s
.
_____________________________________________________________________________________________
Note that if a matrix is in
Reduced Row Echelon Form
then it must also be in
Echelon form.
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To Determine if a Matrix is in
Echelon
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 Fall '11
 Kutter
 Algebra, Row echelon form, reduced row echelon

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