3 a. Which of the following subspaces of U are invariant under D? (i). , (ii). , (iii). , (iv). . b. Determine all 1-dimensional linear subspaces of U invariant under D. 27 In the vector space of...

3

Extracted text: a. Which of the following subspaces of U are invariant under D? (i). <1>, (ii). <1, a="">, (iii). < cos="" a="">, (iv). < cos="" z,="" sin="" a="">. b. Determine all 1-dimensional linear subspaces of U invariant under D.


Extracted text: 27 In the vector space of differentiable functions from R to R we consider the linear subspace U =< cos="" r,="" sin="" r,="" r,="" 1="">. The linear map D: U + U is given by differentiation: (Df)(r) = f'(x).