- #1

killpoppop

- 13

- 0

**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.

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.