1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Polynomials vector space

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    find the rank and nullity of the linear transformation T:U -> V and find the basis of the kernel and the image of T

    2. Relevant equations
    U=R[x]<=5 V=R[x]<=5 (polynomials of degree at most 5 over R), T(f)=f'''' (4th derivative)

    3. The attempt at a solution
    Rank = 2
    Nullity = 4

    basis of kernel = {1,x,x^2,x^3} ?
    since a kernel is mapped to V, then the image is the zero vectors? and the basis of the image of T is the empty set?
  2. jcsd
  3. Feb 4, 2010 #2


    User Avatar
    Homework Helper

    The basis for Im(T) can be {1, x}.
  4. Feb 4, 2010 #3
    another QUESTION

    T : U -> V

    and the kernel(T) is the zero vectors,
    then what is the basis? it's not the empty set?
  5. Feb 4, 2010 #4


    User Avatar
    Homework Helper

    If it happens, for some linear transformation T, that ker(T) = {0} holds, then yes, the basis for ket(T) is the empty set.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook