Page 11 - 35Linear Algebra

1.1 Organizing Information 11

   
1 1

2
2
Denote V by 24 80 35 and thus write V   = 24 80 35  
3 3
B
to remind us to calculate 24(1) + 80(2) + 35(3) = 334

because we chose the order G A N and named that order B
 
s G
so that inputs are interpreted as  s A  .
s N

If we change the order for the variables we should change the notation for V .

   
1 1

Denote V by 35 80 24 and thus write V   = 35 80 24  
2
2
3 3
B 0
to remind us to calculate 35(1) + 80(2) + 24(3) = 264.
0
because we chose the order N A G and named that order B
 
s N
so that inputs are interpreted as  s A  .
s G

0
2
The subscripts B and B on the columns of numbers are just symbols reminding us
of how to interpret the column of numbers. But the distinction is critical; as shown
above V assigns completely different numbers to the same columns of numbers with
different subscripts.
There are six different ways to order the three companies. Each way will give
different notation for the same function V , and a different way of assigning numbers
to columns of three numbers. Thus, it is critical to make clear which ordering is
used if the reader is to understand what is written. Doing so is a way of organizing
information.

2 0
We were free to choose any symbol to denote these orders. We chose B and B because
we are hinting at a central idea in the course: choosing a basis.

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