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Deepak Patra posted an Question
November 06, 2021 • 17:07 pm 30 points
  • IIT JAM
  • Mathematics (MA)

32. let v be the vector space of polynomials in the variable t of degree at most 2 over r. an inner product on v is defined by g.g)-fo)ø(dt for f.g e v. let w s

32. Let V be the vector space of polynomials in the variable t of degree at most 2 over R. An inner product on V is defined by G.g)-FO)ø(dt for f.g E V. Let W span{1-t2,14+t} and W be the orthogonal complement of W in V. Which of the following conditions is satisfied for all h E W-2 1. h is an even function, i.e. h(t) = h(-) 2. h is an odd function, i.e. h(t) =-h(-t) 3. hCt)= 0 has a real solution 4. hC0) = 0

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