(adsbygoogle = window.adsbygoogle || []).push({}); 1. Suppose V,W are vector spaces over a field F and that T: V ---> W is a linear transformation. Show that for any v belonging to V that T(-v) = -T(v)

2. -T(v) denotes the additive inverse of T(v)

3. I think i'm really overcomplicating it =/ But i have

0v = T( v - v ) = T(v) + T(-v)

Then add -T(v)

0v + -T(v) = T(v) + T(-v)

(T(v) + T(-v)) -T(v) = T(v) + T(-v)

then

T(-v) = T(v) + T(-v)

then i suppose it could go to

T(-v) = 0v

but that doesn't help i'm going round in circles. Basically i need a starting point.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof involving vector spaces and linear transformations

**Physics Forums | Science Articles, Homework Help, Discussion**