【題組】10.(10%) Which of the following statements are true?
 
(A) Let D:V -V be defined by D

, where V is the space of functions with basis {sint,cost}. Theeigenvalues of D are ±1.
(B) F is linear if F:R3 → R2 is defined by F(x,y,2) = (x + 1,y + 2).
(C) Assume e that

has two distinct eigenvalues, λ1 andλ2. If dim(

)=n-1, A isdiagonalizable.
(D)

(E) Let Tbe a diagonalizable linear operator on a finite-dimensional vector space, and let m be any positive integer.Tand Tm are simultancously diagonalizable.