試題詳解

複選題
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}. The eigenvalues 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 is diagonalizable.
(D)
(E) Let Tbe a diagonalizable linear operator on a finite-dimensional vector space, and let m be any positive integer. Tand T^m are simultancously diagonalizable.