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$a_0\times1+a_1x+a_2x^2+a_3y+a_4y^2+a_5xy=b_0\times1+b_1x+b_2x^2+b_3y+b_4y^2+b_5xy$
#左邊是取basis的係數
#右邊是任意span的雙變數的多項式
$\forall b_0-b_5,\exists a_0-a_5 s.t. a_0=b_0,a_1=b_1,...,a_5=b_5$
Consider
$a_0\times1+a_1x+a_2x^2+a_3y+a_4y^2+a_5xy=0$
it is trivial to see that $a_0=a_1=a_2=a_3=a_4=a_5=0$ is the only solution.