試題詳解

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.