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.

9. (10%) Which of the following statements are true?(A) Let A and B be n✖ n matrices. Assume that A is invertible and B3 = 0. If AB=BA, then A+B is also invertible. (B) Let S be the set of all sequences in R∞ which have exactly N non-zero elements where N is a known constant. S is a subspace of  R∞. (C) Any square matrix A can be represented as a sum of a symmetric matrix and a skew-symmetric matrix. (D) If A and B are similar, they have the same eigenvectors. (E) If A, B rank (A- B) ≤ rank( A )-rank( B )

110年 - 110 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數、離散數學)#102151

109年 - 109 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數和離散數學)#105828

108年 - 108 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數和離散數學)#106050