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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- Feb 22nd 2010, 04:15 PMp00ndawghelp 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?

- Feb 23rd 2010, 05:05 AMHallsofIvy
Start by writing out what "translations" and "scalings"

**mean**. If T is a translation, on $\displaystyle R^n$, 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 $\displaystyle S(x_1, x_2, ..., x_n)= (ax_1, ax_2, ..., ax_n)$. Just do the calculations for TS and ST.