8. (10pts) Let V and W be finite dimensional vector spaces and let T : V→ W be a linear map. Recall that there exists a unique linear map T
t : W*→ V*, called the transpose of T, where V* and W* are the dual spaces of V and W, respectively.
Consider V = R
2 and W = R
3. Let T : V → W be the linear map defined by
T(a,b)=(3a+6,a-26,2a-6)
Then there exists a unique linear map T
t : W* →V* as above. Define
by
Hint: you need to either explicitly write down T
t(θ)(a,b) for any (a,b)
, or simply write down a 2 x 1 matris representing T
t(θ).
阿摩線上測驗
登入