The vectors \(\mathbf a\), \(\mathbf b\), \(\mathbf c\) and \(\mathbf d\) in \(\mathbb R^3\) are given by

\(\mathbf a=\begin{pmatrix}1\\2\\1\end{pmatrix},\quad \mathbf b=\begin{pmatrix}2\\9\\0\end{pmatrix},\quad \mathbf c=\begin{pmatrix}3\\3\\4\end{pmatrix},\quad \mathbf d=\begin{pmatrix}0\\-8\\3\end{pmatrix}.\)

(i) Show that \(\{\mathbf a,\mathbf b,\mathbf c\}\) is a basis for \(\mathbb R^3\).

(ii) Express \(\mathbf d\) in terms of \(\mathbf a\), \(\mathbf b\) and \(\mathbf c\).