The problem: V=

, T(a,b)= (2a+b, a-3b), x= (3,5). Evaluate T* at the given vector in V.

Thoughts:

I solved this by putting T in matrix form (

) finding

(

) and computing

which equals

.

Uh?? And how do you *actually* find what is?? __This__ is the problem in this question! Yet if we remember that is easily representable by means of when we choose an orthonormal basis for our vector space then the problem is easy. Tonio
I believe this method to be correct (though I wouldn't really be shocked if you told me it wasn't), however, I'd like to be able to solve this problem using the property

because it is my understanding that this is the only way to solve some of these problems. But I can't figure out how this is possible despite at least an hours attempt. *bangs head against wall*