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Math Help - Linear Map Example

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    Linear Map Example

    Example: Determine whether there exist a linear map in T:V_3-->V_3 such that T(0,1,2)=(3,1,2) and T(1,1,1)=(2,2,2) and if exist the give general formula.
    I need solution.
    Thanks...
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    Quote Originally Posted by kjchauhan View Post
    Example: Determine whether there exist a linear map in T:V_3-->V_3 such that T(0,1,2)=(3,1,2) and T(1,1,1)=(2,2,2) and if exist the give general formula.
    I need solution.
    Thanks...

    Complete \{(0,1,2)\,,\,(1,1,1)\} to a basis of V_3 (whatever this linear space is), and then define T on the first two vectors above as you were given, and on the third vector that you'll find define T as you like (say, send that vector under T to zero).
    This is part of a very important theorem that states: a linear map is uniquely and completely determined by its values on any basis of the definition space.

    Tonio
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