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The matrix in (1.1) is in reducedrowechelon form (or rref for short). This is characterized
by the following properties:
•
If a row has nonzero entries then the Frst nonzero entry is 1, which is called the
leading 1
in this row.
•
If a column contains a leading 1 then all other entries in that column are zero.
•
If a row contains a leading 1 then each row above it contains a leading 1 further to the left
of it.
Example 2.
The matrix
0
@
01203
00014
00000
1
A
is in rref.
Example 3.
The matrix
0
B
B
@
12020
00130
00140
00001
1
C
C
A
is not in rref since there is a column that contains
two leading 1’s.
Example 4.
Why is
0
@
1203
0000
0012
1
A
not in rref?
The goal then is to use the following three rowoperations in a systematic manner so that
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 Spring '10
 STAFF
 Linear Algebra, Algebra

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