(5%) Which of the following is true?
(A) Every nonzero subspace of Rⁿ has a unique basis.
(B) Every subspace of Rⁿ has a basis composed of standard vectors.
(C) The column space of an m✖ n matrix is contained in Rm.
(D) If V is a subspace of dimension k, then every generating set for V contains exactly k vectors.
(E) The pivot columns of a m ✖ n matrix A form a basis for the column space of A.

12. (10%) Let M be a subset of R3 containing two or more vectors. Then: (A) The span of any two vectors in M is a plane in R3 (B) Every vector in M is in the span of M (C) If M contains more than threc vectors, then M is linearly independent (D) The span of any two nonzero vectors in M is a plane in R3 (E) None of the preceding statements is true

(5%) Let For what valuc(s) of h is b in the planc spanned by al and az? (A) 0 (B) -10 (C) 16 (D) -17 (E) 20

複選題Which of the following sets is basis (are bases) for R3? (A){10,1,0]T,[0,0,1]T,[1,0,0T}. (B){-2,4,-6]T,[1,-2,3]T}. (C){|0.14,0, -0.1]T, [-1,-0.2,0.4]T,[0.5,0.5,-1)T} (D) {1-1,2,3]T, [8,-7,6]T, [4,-2,3]T,[9,0,5]T}, (E) None of the above are true.

(5%) Find the dimension of the subspacc (A) 2 (B) 3 (C) 4 (D) 1 (E) 0 

複選題Consider the vector space S consisting of all degree-2 polynomials with real coefficients, ie., polynomials in the form of c0 +c1t +c2t2. Define the inner product between two vectors as c2d2. Which of the following statement is/are true? (A). The dimension of S is 2. (B). The polynomials 1 + t, t and 1 + t2 are linearly independent. (C). The set{1 + t, t, 1 + t2} can be a basis for S. (D). The two polynomials 1 - 2t + t2, and -1 + 2t - t2 are orthogonal to cach other. (E). None of the above is true.

複選題Find a basis of U, if exist, U ={f(x)|f(x)=a+bx+cx2+dx3},p3 =span{1,x,x2,x3}.(10% (A) f(2)=0(B)f(1)=5(C)a+b=c+d, a=2d

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2 「政府推行劫富濟貧的社會福利政策是強盜的行為」這樣的推論邏輯有什麼問題？ (A) 目的論（teleology） (B) 套套邏輯（tautology） (C) 區位（ecological）謬誤 (D) 沒有問題

3 那一種研究取向，認為「常識是比較無效的知識，科學才是知識有效性的保證」？ (A) 實證論 (B) 詮釋論 (C) 批判論 (D) 後現代社會研究

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