# Proving linear transformation maps 0 to 0

• Aug 20th 2011, 04:51 AM
Glitch
Proving linear transformation maps 0 to 0
Suppose that T : V -> W is linear. Prove that T(0) = 0.

Not sure how I'm supposed to prove this. I know that transformations are supposed to preserve the zero vector, but I can never get my head around proving these things. I'm guessing it has something to do with preserving scalar multiplication and vector addition? What should I do?

Thanks.
• Aug 20th 2011, 05:30 AM
Traveller
Re: Proving linear transformation maps 0 to 0
Hint: T(0) = T(0+0)
• Aug 20th 2011, 06:45 AM
FernandoRevilla
Re: Proving linear transformation maps 0 to 0
Another way: $T(\vec{0})=T(0\cdot\vec{0})=\ldots$ .