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Math Help - help with translations

  1. #1
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    help with translations

    Show that translations and scalings commute among themselves but not with each other; i.e., T T' = T' T and S S' = S' S but T S and S T are generally not equal. how can i show that they are generally not equal?
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    Quote Originally Posted by p00ndawg View Post
    Show that translations and scalings commute among themselves but not with each other; i.e., T T' = T' T and S S' = S' S but T S and S T are generally not equal. how can i show that they are generally not equal?
    Start by writing out what "translations" and "scalings" mean. If T is a translation, on R^n, say, then [tex]T(x_1, x_2, ..., x_n)= (x_1+ a_1, x_2+ a_2, ..., x_n+ a_n). A "scaling" is of the form S(x_1, x_2, ..., x_n)= (ax_1, ax_2, ..., ax_n). Just do the calculations for TS and ST.
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