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Math Help - Find a linear transformation

  1. #1
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    Find a linear transformation

    Is there a linear transformation T:R^3 \rightarrow R^2 such that T(1,0,3) = (1,1) and T(-2,0,-6) = (2,1)?

    I set the system of 1x+3y = 1 and -2x + -6y = 2 in an attempt to find x and y, but it turns out to be no solution, does that means there is no linear transformation in this case?
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    Quote Originally Posted by tttcomrader View Post
    Is there a linear transformation T:R^3 \rightarrow R^2 such that T(1,0,3) = (1,1) and T(-2,0,-6) = (2,1)?

    I set the system of 1x+3y = 1 and -2x + -6y = 2 in an attempt to find x and y, but it turns out to be no solution, does that means there is no linear transformation in this case?
    Sounds about right to me.

    -Dan
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    I thought more about this problem and I realized the solution.

    (-2)(1,0,3) = (-2,0,-6) but then (-2)T(x)  \neq T(-2x).

    Good, problem solved, thank you.
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