Prove a given transformation exists or not: T: R^4 -> R^5

[daniel_i_l]

Homework Statement

Prove if the following transformation exists or not: T: R^4 -> R^5
where: KerT=Sp{(0,1,1,0),(1,1,0,0)} , ImT=Sp{2,3,4,0,0),(1,1,0,0,0),(0,1,1,0,0)}

Homework Equations

T:V->W
dimImT + dimKerT = dimV

The Attempt at a Solution

I think that the answer is no because dimKerT=2 , dimImT=3 but 2+3 =/= 4.
Is that right? Am I missing something?
Thanks.

 

[Dick]

Yes, it's right. No, you aren't missing anything.