# Express basis in terms of a subspace of functions

So I have a subspace of the form W = {a$e^x$ + b$e^{-x}$} and I need to express the basis {$e^x$+$e^{-x}$, $e^x$-$e^{-2x}$}

How can I express the second argument of the basis taking into account the 2 in the exponent of e?

I know that the first argument would be a vector of the form (1,1) and the second would start (1, -?);

• What do you mean by "express the base"? These two bases clearly correspond to different subspaces, since $$ae^x + b^{-x} = e^x - e^{-2x}$$ implies $a=1$ and $b=-e^{-x}$ - which is not a scalar! – Math1000 Nov 28 '16 at 18:38
• @Math1000 express the basis, already edit it – ravelinx Nov 28 '16 at 18:42
• @Math1000 the two bases form a basis that belongs to W – ravelinx Nov 28 '16 at 18:44
• Now the question makes even less sense... – Math1000 Nov 28 '16 at 18:46