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Math Help - Transformations of Variables

  1. #1
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    Transformations of Variables

    I need to find the image of a line under a specific operator, but there are 4 variables, two of which are direct results of a transformation.

    Suppose that T maps (x,y) into (s,t) is the linear operator on R2 defined by the equations:
    2x+y=s
    6x+2y=t

    Find the image of the line x+y=1 under this operator.

    Well, I know that the standard matrix is
    2 1
    6 2

    but how do I find the image of x+y=1?
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    I need to find the image of a line under a specific operator, but there are 4 variables, two of which are direct results of a transformation.

    Suppose that T maps (x,y) into (s,t) is the linear operator on R2 defined by the equations:
    2x+y=s
    6x+2y=t

    Find the image of the line x+y=1 under this operator.

    Well, I know that the standard matrix is
    2 1
    6 2

    but how do I find the image of x+y=1?
    y = 3s - t
    x = -s + \frac{1}{2} t
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    How did you get that? It looks like you divided by 2 somewhere, but I'm not sure...
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    Quote Originally Posted by Hellreaver View Post
    How did you get that? It looks like you divided by 2 somewhere, but I'm not sure...
    I treated

    2x+y=s
    6x+2y=t

    as simultaneous equations and solved for x and y in terms of s and t.
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  5. #5
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    Oh, ok, I see what you did... Now would I have to put those values into x+y=1?
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    Quote Originally Posted by Hellreaver View Post
    Oh, ok, I see what you did... Now would I have to put those values into x+y=1?
    Well I sure didn't find them because they'd look pretty on the mantlepiece ......
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