複選題 (5%) Which of the following lists of vectors in R3 are linearly dependent? (A)u=(1,2,5),t(2,5,1),u元(5,2,1) (B)u=(1,2,5), =(1,5,6), w=(0, 0, 0) (C)น=(2,-4,8),=(3 ,-6, 12),w=(1,2,6) (D)u-(1,2,3),=(4,5,6),w=(1,4,6),x-(3,4,6)

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
(5%) Which of the following lists of vectors in R³ are linearly dependent?
(A)u=(1,2,5),t(2,5,1),u元(5,2,1)
(B)u=(1,2,5), =(1,5,6), w=(0, 0, 0)
(C)น=(2,-4,8),=(3 ,-6, 12),w=(1,2,6)
(D)u-(1,2,3),=(4,5,6),w=(1,4,6),x-(3,4,6)

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