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: If Ker T != 0 then T is not isomorphism

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that if ker T != 0 then T is not an isomorphism.

    2. Relevant equations

    3. The attempt at a solution
    If Ker T != 0 that means that there are multiple solutions for which T=0 meaning it is not injective and hence not isomorphic? Is that correct? I don't think it is, or is there a better way of proving this? Thanks.
  2. jcsd
  3. Oct 24, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well, it is correct. If x is a nonzero element of ker T, then Tx=0=T0. Not injective. Not isomorphism.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook