43
GaussJordan Elimination
We will do
row operations
:
1.
Interchange two rows
R
i
R
j
2.
Multiply a row
by a constant
cR
i
R
i
3.
Add a multiple of one row
cR
i
+ R
j
R
j
to another
•
on an
augmented matrix
to solve a system
•
using a method known as
G
AUSS
J
ORDAN
E
LIMINATION
:
1.
Get a 1 in upper left corner (by row ops 1 and/or 2)
2.
Get 0's everywhere else in its column (by row op 3)
3.
Mentally delete row 1 and column 1. What remains is a
smaller
submatrix
.
4.
Get 1 in upper lefthand corner of the
submatrix
.
5.
Get 0's everywhere else in its column for
all rows
in the
matrix (not just the submatrix).
6.
Mentally delete row 1 and column 1 of the submatrix,
forming an even smaller submatrix.
7.
Repeat 4, 5, 6 until you can go no further.
8.
The matrix will now be in
reduced rowechelon form
(RREF), or just
reduced form
.
6.
Rewrite the system in natural form.
7.
State the solution.
A.
If you get a row of all zeros, use row op 1 to make it the
last row
B.
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 Spring '11
 Staff
 GaussJordan Elimination, Gaussian Elimination, Mentally delete row

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