31. If ||u||= 8 and ||v|| = 3, then what are the largest possible values of the inner product (u + v,v)?
(A) 24
(B) 12
(C) 15
(D)33
(E) 45

32. Consider the system of linear equations:For what value of C will the system be singular? (A)-10 (B)-6 (C) -3 (D) 4 (E) 10

33. Given the row-reduced echelon form of a matrix A. What is the closest vector to b = [0,3,0, 1]T in the row space of A? (A) [1,1,2,0]T (B) [0,-2,-1,1]T (C) [-1, 2,0, -1]T (D) [-1,2,1,0]T (E) [1,1,3,1]T

34. Let ， which of the following statement is incorrect? (A) The rank of A is 3. (B) The inverse matrix is (C) If we define the characteristic polynomial of A is f(t)=det(A-tIn), then f(1)=-t3+3t2+3t-1. (D) One of the eigenvalues is -1 and the corresponding eigenvector is (-2, 1, 2)T. (E) The matrix cannot be diagonalized over the real field.

35. An n x n skew-symmetric matrix A is defined as At= -A. Please find the dimension of this matrix. (A)n (B) n2 (C) n(n + 1)/2 (D)n(n-1)/2 (E) n +1 

36. A vector space is spanned by {1,cos(t),sin(t)} for -π≤t≤π . If a vector: v=a.1+b.sin(t)+cㆍcos(t) is the closest vector in this vector space to a continuous function: f(t)=t for -π ≤t≤π, what is this closest v? The inner product of two continuous functions: fand g within [a, b] is defined by You may need the following integral:. (A)v=1+2sin(t)-2cos(t) (B) v=1-2cos(t) (C) v= 2sin(r) (D) v=1+2sin(t) (E) v=-2cos(t)

37. A quadratic equation is described as: x2 +8xy + 7y2 = 225. Which of the following statement is incorrect? (A) The curve is centered at the origin (B) This quadratic curve is an ellipse (C) One of the principal axes is (D) The other principal axis is (E) The shortest distance from this quadratic curve to the origin is 5

38. Which of the following statements is true? (A) Let A be an arbitrary matrix of size m X n. If m ＞ n, then rank( A ) ＜ rank(At). (B) Let A be an arbitrary matrix of size m ✖n. If m ＞ n,then rank( A ) ＞ rank(At). (C) If W1, W2 are two subspaces of V, then the union W1U W2 is also a subspace of V. (D) Let W be a subspace of a vector space V. Then, dim(W) ≤ dim(V). (E) Let A be a square matrix, k be a constant. Then, det(kA) = kdet( A ).

39. Consider the matrix . How many different mattices are there such that B2 = A? (A) 0 (B) 1 (C) 2 (D) 4 (E) 16

40. Consider the Fibonacci series a0 = 1, a1 = 2,and an = an-1 + an-2 for any n≥ 2. Therefore, we have {an} = {1,2,3,5,8, ...}. The general expression for an as a function of n can be found via the following method； first, definc , and an define the state vector . Thus, we have the initial condition ，and  the relation Vn+1 = Avn. The following general expression can be derived: an = are the eigenvalues of A. How many ofthe following statements are true? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

151. The following information is given about a group of high-risk borrowers.i) Of all these borrowers, 30% defaulted on at least one student loan.ii) Of the borrowers who defaulted on at least one car loan, 40% defaulted on at least one student loan.iii) Of the borrowers who did not default on any student loans, 28% defaulted on at least one car loan.A statistician randomly selects a borrower from this group and observes that the selected borrower defaulted on at least one student loan.Calculate the probability that the selected borrower defaulted on at least one car loan.(A) 0.33(B) 0.40(C) 0.44(D) 0.65(E) 0.72

114年 - 114 國立清華大學學士後醫學系單獨招生考試_學士後醫學系/智慧資訊科技組：資訊科學#135660

113年 - 113 國立清華大學學士後醫學系單獨招生考試_學士後醫學系/智慧資訊科技組:資訊科學#119923

112年 - [非官方正解]國立清華大學 112 學年度學士後醫學系單招試題 考試科目：資訊科學#120021

111年 - 111 國立清華大學學士後西醫學系單獨招生考試_學士後醫學系/智慧資訊科技組:資訊科學#110534