Gauss-Jordan - page 1
Gauss-Jordan Elimination
I. A linear system such as can be solved by hand algebraically or by using an
x5yz11
3z12
2x4y2z8
+−=−
=
+−=
augmented matrix and elementary row operations.
A. Elementary row operations that produce row-equivalent matrices
1. Two rows are interchanged
ij
RR
↔
2. A row is multiplied by a nonzero constant
ii
kRR
→
3. A constant multiple of one row is added to another row
jii
kRRR
+→
(NOTE:means"replaces")→
II. Performing elementary row operations on the TI-83
The result of a row operation is displayed on the home screen, but it is not automatically stored!
You should immediately store the result under a different name. It is convenient (and frequently
useful) to store the results alphabetically.
A. Row swap
To interchange rows 1 and 3 of matrix A:
MATH C:rowSwap( MATRIX ENTER MATRIX
NAMES 1:[A]
ENTER,1,3)
NAMES 2:[B]
ENTER STO$MATRIX ENTER
B. Multiplying a row by a nonzero scalar
To multiply row 1 of matrix A by :
1
3
MATH E:*row(
MATRIX ENTER 1
3, MATRIX
NAMES 1:[A]
ENTER , 1 ) ENTER
NAMES 3:[C] STO$MATRIX ENTER
C. Adding a nonzero scalar multiple of one row to another row
To multiply row 2 of matrix A by and add it to row 3
1
2
−
(of matrix A):
MATH F:*row+(
MATRIX ENTER 1
2
−, MATRIX
NAMES 1:[A]
ENTER , 2 , 3 ) ENTER
NAMES 4:[D]
STO$MATRIX ENTER
