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.

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
Which of the following sets is basis (are bases) for R3?
(A){10,1,0]^T,[0,0,1]^T,[1,0,0^T}.
(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.

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