Prachi kashyap Asked a Question
January 31, 2022 12:37 pmpts 30 pts
19. Let V be a vector space of all real valued functions from (-1, 1)> R. W-feVIf(x) = f(-x), Vx e (0, 1)) W, ={fe VIf(-x) =-f (x), Vx e (0, 1)} Let T: V>V linear operator such that T(w, + uw,) = w, - w, Vw, e W, w, e W2 then choose the incorrect? (a) T is not Invertible (b) T is Involuntary (c) ker(T - I)n ker (T + I) = {0} (d) Im(T-I)n Im(T + I)= {0}
  • 1 Answer(s)
  • 0 Likes
  • 2 Comments
  • Shares
  • Prachi kashyap
    how u take T^2 =I
    Likes(1) Reply(1)
    Piyush pachauri
    apply T on w1-w2 = w1+w2
  • Piyush pachauri thankyou
    This is reflection. T^2=I T is invertible because it doesn't have 0 Eigen values , possible Eigen values are 1 and -1
    Likes(0) Reply(0)