profile-img
Shamsun posted an Question
August 27, 2020 • 21:32 pm 30 points
  • IIT JAM
  • Mathematics (MA)

9 let v, = (1, 0) v, = (1, -1) and v, = (0, 1), then how many linear transformations t: rr are there such that t(v,) = v t(v) = v t(v) = v,?

9 Let v, = (1, 0) v, = (1, -1) and v, = (0, 1), then how many linear transformations T: RR are there such that T(v,) = V T(V) = V T(v) = V,?

3 Answer(s) Answer Now
  • 1 Likes
  • 8 Comments
  • 0 Shares
  • Shashi ranjan sinha

    in case of R² into R², again there doesn't exist any such linear transformation... see the attachment

    cropped1092714304148376283.jpg
    eduncle-logo-app

    but solutions is three

    eduncle-logo-app

    are you sure that the domain is R²?.... because in that case , you can see in the above attachment that there doesn't exist any linear transformation satisfying the given conditions

    eduncle-logo-app

    yes domain is R^2

    eduncle-logo-app

    okk.... then in that case, go with the above which shows that if we assume T be the linear transformation satisfying the given conditions, then we will have a contradiction....hence there doesn't exist any such linear transformation

  • Shashi ranjan sinha best-answer

    There doesn't exist any such linear transformation.... T is from R³ into R²... since V1, V2, V3 are vectors in R², so T cannot maps them as these vectors don't belong to their domain

    eduncle-logo-app

    printed mistakes ..T:R^2 to R^2

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers