[ 6 marks] For the following linear operators, flind one invariamt subspace of the givea dimescion.
(a) For
D:P_(3)(R)->P_(3)(R)
, the differentiation operator (so
D(p(x))=p^(')(x)
), find an invariant subspace of dimension 2 .
(b) For
S:C^(2)->C^(2)
give by
S(v)=[[1,2],[-1,3]]v
, find an invariant subspace of dimension 1 .
(c) For
T
:
M_(2\times 2)(R)=>M_(2\times 2)(R)
, given by
T(A)F^(T)A^(T)
End an invariant subepace of dimension 3 .