Let $\mathcal{P}_2$ be the vector space of all polynomials of degree 2 or less, and let $H$ be the subspace spanned by $21x-14x^{2}-10, \ 10x-7x^{2}-5$ and $14x^{2}-19x+10$.

1. The dimension of the subspace $H$ is .
   
   
2. Is $\lbrace 21x-14x^{2}-10, 10x-7x^{2}-5, 14x^{2}-19x+10 \rbrace$ a basis for $\mathcal{P}_2$? choose basis for P_2 not a basis for P_2 Be sure you can explain and justify your answer.
   
   
3. A basis for the subspace $H$ is $\big\lbrace$ $\big\rbrace$. Enter a polynomial or a comma separated list of polynomials.