19. (3%) If det ，what is the value of k?
(A) 2
(B) 3
(C) 4
(D) 6

20. (3%) Which of the following statements is true? (A) If none of the vectors in the set S = {v1, v2,v3} in R3 is a multiple of one of the other vectors, then S is linearly independent. (B) If A is a subspace, then its complement is also a subspace. (C) If a square matrix A has independent columns, so does A2. (D) Every vector space has at least two distinct subspaces.

21. (3%) Which of the following statements is a linear transformation?  (A) L(x,y,z) = (x + y,y2,2z)(B) (C) (D) L(x,y,z) =

22. (3%) Which of the following statements is true? (A) A square matrix with linearly independent column vectors is diagonalizable. (B) If A and B are diagonalizable, so is AB. (C) If A bc diagonalizable and AB = BA, then B is diagonalizable. (D) If A is a 3 ✖3 matrix with distinct eigenvalues 0,1,2, then the matrix (A + I) must be invertible.

23. (3%) Which of the following statements is true? (A) Let S be a subset of a vector space. Then S = (B) Let V be a subset of Rn, and if V is orthogonal to W, then is orthogonal to. (C) If u and v are vectors in Rn, and if distance from u to v equals the distance from u to -v, then and v are orthogonal. (D) If u, v and w are vectors in Rn, and if u is orthogonal to v +w, then u is orthogonal to v and w.

24. (3%) Given the following data points{(-1,1),(1,3),(2,3)}, supposc that the lincar function y =x is the approximation to fit the data in the least squares sensc, please find the value of (a+ b+ c+ d) mod 11. (A) 1 (B) 3 (C) 7(D) 10

25.(3%) Let S=spanf{(1 3 1 1)T,(1 1 1 1)T,(-1 5 2 2)T} be a subspace of R4. Suppose w1= , is aothonormal basis of S. Please find the value of (a1 + a2 + a3 + a4)+ (b1 +b2 +b3 +b4)+(c1+c2 +c3 +c4)? (A) 5 (B) 6 (C) 7 (D) 8

1. 根據迪摩根（DeMorgan’s Law），下列何者是錯誤的？ (A) (X+Y)’=X’Y’ (B) (XY)’=X’+Y’ (C) (X+Y+Z)’=X’Y’Z’ (D) (XY’+Z)’=(Y’+X)Z’

2. 8051 有幾個輸入輸出埠？ (A) 1 個 (B) 2 個 (C) 3 個 (D) 4 個

3. 若將 5 安培的電流源接於 1 歐姆電阻與 R 歐姆電阻並聯，且流經 1 歐姆的電流為 4 安培，請問 R 值為多少？ (A) 4 歐姆 (B) 3 歐姆 (C) 2 歐姆 (D) 1 歐姆

4. 下列何者不是負回授放大器的性質？ (A) 提高增益的靈敏度 (B) 增大頻帶寬度 (C) 降低非線性失真 (D) 提高訊號雜訊比

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_資訊科學系:計算機數學#108089