Hint: T(0) = T(0+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.