# Math Help - linear transformation

1. ## linear transformation

Determine a linear transformation T:V2->V2 , which maps all the vectors on the line x+y = 0 onto thmeselves (T is not I).

2. Originally Posted by reha
Determine a linear transformation T:V2->V2 , which maps all the vectors on the line x+y = 0 onto thmeselves (T is not I).

$x+y=0\Longleftrightarrow y=-x\Longleftrightarrow$ the vector $(1,-1)$ , generator of the above line, must be mapped either to himself or to another vector in the same line, so you can try $T(x,y):=(y,x)$ . Now check T is a lin. trans. and it maps the above line to itself.

Tonio