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 )

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 Tm are simultancously diagonalizable.

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