NAMING ELEMENTARY ROW OPERATIONS

An elementary row operation is
is one of the following changes
made to the rows of a matrix:
[1]
Interchanging two rows
[2]
Multiplying or dividing each element of a row
by the same non-zero number "c".
 
[3]
Adding to a row (the TARGET ROW) a non-zero
multiple "c" of another row (the TOOL ROW).

PROF McFARLAND's NAMES FOR ROW OPERATIONS DIFFER A BIT from names used in our text: compare both in the table below. In the left column (Prof McFarland's) small r is used for rows in the (old) matrix about to be altered. Capital R is used to name the newly altered row in it's newly created matrix.

Prof McFarland's Names Row Operation Text's Names
[1] rm rn
or
Rm = rn and Rn = rm
Interchange
rows rm and rn
Rm Rn
[2]
Rm = c rm
or
Rm = rm
Multiply
or
Divide		   by c
c Rm Rm
or
Rm Rm
[3] Rm = rm + c rn
Add a Multiple
of Row n
to Row m		 Rm + c Rn Rm

An example of how row operations should look is shown below, with all rows color coded (black/green/magenta/brown/blue) to show the match-up between matrix rows and their names.


3		   -1
2		 2
11		 R2 = r2 - 3r1
 1
0		   -1
 2
5		 R2 = (0.2)r2
 1
0		   -1
1		 2
1		 R1 = r1 + r2
 1
0		   0
1		 3
1
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