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Math Help - Invertible & examining the image through the unit square

  1. #1
    Member thaopanda's Avatar
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    Invertible & examining the image through the unit square

    let f : R^2 \rightarrow R^2 be defined by f(x,y) = (x+y, 2x+ay) where a \in R is a constant.

    (a) Show that df(x,y) is invertible if and only if a \neq 2
    (b) Examine the image through f of the unit square Q :={(x,y) \in [0,1] x [0,1]} when a=1, a=2, and a=3

    So.. I don't understand how to show it's invertible or what (b) even means...
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  2. #2
    Senior Member Shanks's Avatar
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    Notice that f is a linear transformation.
    for(1), you need to find the matrix correspondding to f.
    for(2), find the four image of the four vertex of each unit square.
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  3. #3
    Member thaopanda's Avatar
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    yeah... if I learned that, I don't recall it...

    I'm still lost
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