4.(25%) Let P2 denote the vector space of all polynomials of degree less than 2. (Consider the transformation L:P2 →R2 defined by L(p(x)): = with undecided parameters a>0 and . Let A be the matrix representation of transformation L with respect to the ordered bases E = [I, x] and E'= for P2 and R2, respectively.
以下小題僅需依序寫下答案即可,不需做任何推導。
(4.2) Let's define an inner product for P2 by <p(x),q(x),for arbitrary and γ≠I an undecided parameter. Find the orthonormal basis, denoted by F := [f1, f2], of P2, generated from basis E given above to satisfy the subspace equality constraints Span(f1)=Span(I) and Span(f1,f2)=Span(1,x). (8%)