Simple question on non singular linear transformation

  • Thread starter cocobaby
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Homework Statement


Given that "If T(Ta)=0, then Ta=0",
can we say that the linear transformation on V is nonsingular?

Homework Equations





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?
 

Answers and Replies

  • #2
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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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