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Simple question on non singular linear transformation

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data
    Given that "If T(Ta)=0, then Ta=0",
    can we say that the linear transformation on V is nonsingular?

    2. Relevant equations



    3. The attempt at a solution

    Since what the statement implies is that T has only zero subspace of V as its null space, can we not say that it's nonsingular?
     
  2. jcsd
  3. Mar 10, 2010 #2

    Mark44

    Staff: Mentor

    I don't think you can say that at all. Suppose T:V --> V is defined by T(x) = 0 for any x in V. The nullspace of T is all of V, so T is definitely noninvertible. What does that imply about T being singular or nonsingular?
     
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