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Answer:

Can it be done? Yes.

a( -1, 5 )T + 2( 3x, 10 )T = ( 8, 25 )T
 ( -a, 5a)T +  ( 6x, 20 )T = ( 8, 25 )T
         ( 6x-a, 5a+20 )T  = ( 8, 25 )T

Equating corresponding elements:

6x-a  =  8
5a+20 = 25
   5a = 5
    a = 1

6x-1  = 8
6x    = 9
    x = 9/6 
    x = 3/2

Scaling with values less than One

In the definition of scaling:

a( x, y )T = ( ax, ay )T

it is OK if a is smaller than one. For example:

0.5( x, y )T  =  ( 0.5x, 0.5y )T

Sometimes this is written as:

( x, y )T
          =  ( x/2, y/2 )T  
   2

QUESTION 8:

(Review: ) What is the length of (1,0)T ?