Let V = P2(R), give V the inner product defined by (f,g) = Lo s(1)g(t) dt, and let W = span {1 – x}. Calculate f (1 – 1)(a + bx + cx²) dr, and use the direct result of this calculation together with the result of part (a) to find a basis for W+. Show your work, and also make sure to prove that your answer really is a basis for w+.

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A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

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Q: Let T: P₁ → R² be defined by T (P) Let q(t) = 5t6t² +7t³. Find T(q). Find a basis for the kernel of…

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Q: find the orthogonal complement W' of W  and give a basis for W' of the following:  W = {[x y z]:…

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Q: Let V=R₂₂ [x] with (the inner product, 1 <f(x), g(x)) = f(x) g(x) dx Find a basis for the or…

A: Answer is not correct, since the second element is not orthogonal to x2+x+1. Please check and verify…