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

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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