Let $\mathcal{P}_2$ denote the vector space of all polynomials in the variable $x$ of degree less than or equal to $2$. Let $\mathcal{C} = \lbrace -2, 1+2x, -2+3x-2x^{2} \rbrace$ be an ordered basis for $\mathcal{P}_2$.

1. Write $-7+x-2x^{2}$ as a linear combination of elements from the basis $\mathcal{C}$.
   
   $-7+x-2x^{2} =$ $(-2) +$ $(1+2x) +$ $(-2+3x-2x^{2}).$
   
   
2. Let $\lbrack q \rbrack_{\mathcal{C}}$ denote the coordinate representation of $q$ relative to the basis $\mathcal{C}$. Find the coordinate vector representation for $-7+x-2x^{2}$ relative to the basis $\mathcal{C}$. Your answer should be a vector of the general form $\verb+<1,2,3>+$.
   
   $\lbrack -7+x-2x^{2} \rbrack_{\mathcal{C}} =$ .