MA 35100 LECTURE NOTES: WEDNESDAY, JANUARY 20
GaussJordan Elimination
We review some ideas from the last lecture. First, we begin with a formal deﬁnition.
Deﬁnition.
A matrix is in
reduced rowechelon form (rref)
if it satisﬁes all of the
following conditions:
a. If a row has nonzero entries, then the ﬁrst nonzero entry is 1, called the
pivot
in
this row. The variables corresponding to the pivots are called
leading variables
,
and the other variables are called
free variables
.
b. If a column contains a pivot, then all other entries in that column are zero.
c. If a row contains a pivot, then each row above contains a pivot further to the
left.
Recall that in the previous lecture we began with the matrix
A
=
0 0 1

1

1
4
2 4 2
4
2
4
2 4 3
3
3
4
3 6 6
3
6
6
0 0 0
0
0
0
.
and performed a series of steps to arrive at the matrix
E
=
1
±
2
0
3
0
2
0
0
1
± 
1
0
2
0
0
0
0
1
±

2
0
0
0
0
0
0
0
0
0
0
0
0
.
Note that
A
is not in reduced rowechelon form, but
E
is. The pivots are circled in the matrix
above.
Given a matrix
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 Spring '10
 EGoins
 Linear Algebra, Algebra, GaussJordan Elimination, rowechelon form

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