I was wondering how to write $x$ as an algebraic combination of $\{x+xy,y+xy,x^2,y^2\}$, with the coefficients $\in \mathbb Q[x,y]$.
Can $x$ be written as a $\mathbb{Q}[x,y]$-algebraic combination of $x+xy$, $y+xy$, $x^2$, and $y^2$?
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linear-algebra
algebra-precalculus
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0I think that the kind of combination that you want is called an _algebraic_ combination. – 2012-02-05
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0I've revised my answer to include a solution to this new, edited problem. See my post below. – 2012-02-05
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0@alex.jordan Thanks. – 2012-02-05