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Math Help - linear algebra question

  1. #1
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    linear algebra question

    Hi, Suppose T is a linear map from R^2 to R^3 and it satisfies T(1,1) = (1,1,0) and T(2,3) = ( -1,2,1). What is the matrix T and the formula for T(x,y)?

    My troubl with this question is that I cant seem to find a 3 by 2 matrix such that when multiplied by (x,y) gives both vectors in R^3 as above
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ferico View Post
    Hi, Suppose T is a linear map from R^2 to R^3 and it satisfies T(1,1) = (1,1,0) and T(2,3) = ( -1,2,1). What is the matrix T and the formula for T(x,y)?

    My troubl with this question is that I cant seem to find a 3 by 2 matrix such that when multiplied by (x,y) gives both vectors in R^3 as above
    Let T = \left( \begin{array}{cc} a & b \\ c & d \\ e & f \end{array} \right)

    then, T {1 \choose 1} = \left( \begin{array}{c} a + b \\ c + d \\ e + f \end{array} \right) = \left( \begin{array}{c} 1 \\ 1 \\ 0\end{array} \right)

    and

    T {2 \choose 3} = \left( \begin{array}{c}  2a + 3b \\ 2c + 3d \\ 2e + 3f \end{array} \right) = \left( \begin{array}{c} -1 \\ 2 \\ 1 \end{array} \right)

    equating components, we get the systems:

    a + b = 1 .............(1a)
    2a + 3b = -1 .........(2a)

    c + d = 1 ..............(1b)
    2c + 3d = 2 ............(2b)

    e + f = 0 ..............(1c)
    2e + 3f = 1 ...........(2c)


    these are each simultaneous equations that you should be able to solve
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  3. #3
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    But this is precisely the question. I don't know which a and b to choose such that a+b =1 and 2a +3b = -1.
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  4. #4
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    nvm lol i got it "simultaneous equations" i can solve it. Thanks alot for your help
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