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Help with a linear algebra problem

  1. Oct 25, 2006 #1

    Any fuction T: V->W . V and W are vector spaces over the field of rational numbers. The fuction T is called additive if T(x+y)=T(x)+ T(y).

    Proof that any function T from v to w are additive, then it must be a linear transformation.

    2) Let T:V->W be linear

    prove that if T is 1 to 1 IFF T carries linear indep subset in V to Linear, indep subset in W.
  2. jcsd
  3. Oct 26, 2006 #2


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    1. Hint - Write the definition of a linear transformation right next to the question.

    2. Hint - Assume it maps a lin. ind. subset in V to a lin. dep. subset to W.

    That's only one direction, but now you have to go the other way too. (if and only if)
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