試題詳解

36. A vector space is spanned by {1,cos(t),sin(t)} for -π≤t≤π . If a vector: v=a.1+b.sin(t)+cㆍcos(t) is the closest vector in this vector space to a continuous function: f(t)=t for -π ≤t≤π, what is this closest v? The inner product of two continuous functions: fand g within [a, b] is defined by You may need the following integral:.
(A)v=1+2sin(t)-2cos(t)
(B) v=1-2cos(t)
(C) v= 2sin(r)
(D) v=1+2sin(t)
(E) v=-2cos(t)