- #1
killpoppop
- 13
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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.
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.