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Math Help - linear

  1. #1
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    linear

    Let T: V--->W be a linear transformation in which the zero vector in V is the only vector mapped to the zero vector in W by T. Prove that T is injective.
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  2. #2
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    Quote Originally Posted by natewalker205 View Post
    Let T: V--->W be a linear transformation in which the zero vector in V is the only vector mapped to the zero vector in W by T. Prove that T is injective.
    Say that T(\bold{x}) = T(\bold{y}) \implies T(\bold{x} - \bold{y}) = \bold{0} because it is a linear transformation. This means, \bold{x}-\bold{y}  = \bold{0}\implies \bold{x} = \bold{y}.
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