$6 .$ (a) Write the matrix of linear transformation, $T: P_{3} (x) ightarrow P_{2}(x)$ detined by $T\left(a_{0}+a_{1} x+a_{2}x^{2}+a_{3} X^{3} ight)=a_{3}+\left(a_{2}+a_{3} ight) x+\left(a_{0}+a_{1} ight) x^{2}$ Relative to the basis $B=\left\{1, X-1, (x-1)^{2}, (x-1)^{3} ight\}$ and $B=\left\{1, X, X^{2} ight\}$ respectively. \begin{tabular}{1|1|1|1|1|1|1|} \hline (b) (i) If $\mathrm{V}$ is a vector space of all square $\mathrm{n} \times \mathrm{n} m$ & 0 & 0 & $\mathrm{-h}$ & $\mathrm{-g]$ \\ \hline \end{tabular} for a given matrix $M$. Then show that $W$ is a subspace of $V(F)$. (ii) In a complex vector space $V(C)$, show that $(1+i, 1-1) - CS.VS. 1603|