1 The vectors \(\mathbf { a } , \mathbf { b } , \mathbf { c }\) and \(\mathbf { d }\) in \(\mathbb { R } ^ { 3 }\) are given by
$$\mathbf { a } = \left( \begin{array} { l }
1 \\
2 \\
1
\end{array} \right) , \quad \mathbf { b } = \left( \begin{array} { l }
2 \\
9 \\
0
\end{array} \right) , \quad \mathbf { c } = \left( \begin{array} { l }
3 \\
3 \\
4
\end{array} \right) \quad \text { and } \quad \mathbf { d } = \left( \begin{array} { r }
0 \\
- 8 \\
3
\end{array} \right) .$$
- Show that \(\{ \mathbf { a } , \mathbf { b } , \mathbf { c } \}\) is a basis for \(\mathbb { R } ^ { 3 }\).
- Express \(\mathbf { d }\) in terms of \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\).