(b) Let $V(R)$ be a vector space of polynomials over $R$ and $V_{1}, V_{2}$ are subspaces of $V$ spanned by $S_{1}=\left\{x^{3}+4 x^{2}-x+3, X^{3}+5 x^{2}+5,3 X^{3}+10 x^{2}-5 x+5 ight\}$ and $S_{2}=\left\{x^{3}+4 x^{2}+6, X^{3}+2 x^{2}-x+5,2 x^{3}+2 x^{2}-3 X+9 ight\}$ resp. Find (i) dimension $\left(\mathrm{V}_{1}+\mathrm{V}_{2} ight) $ and (ii) dimension $\left(V_{1} \cap V_{2} ight) $ using the dimension theorem. CS.VS. 1599