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