18
\end{array} \right) \quad \text { and } \quad \mathbf { v } _ { 4 } = \left( \begin{array} { r }
0
- 2
10
8
\end{array} \right) .$$
- Show that the dimension of \(V\) is 3 .
- Express \(\mathbf { v } _ { 4 }\) as a linear combination of \(\mathbf { v } _ { 1 } , \mathbf { v } _ { 2 }\) and \(\mathbf { v } _ { 3 }\).
- Write down a basis for \(V\).
Let \(\mathbf { M } = \left( \begin{array} { r r r r } 1 & - 2 & 0 & 0
2 & - 5 & - 3 & - 2
0 & 5 & 15 & 10
2 & 6 & 18 & 8 \end{array} \right)\). - Find the general solution of \(\mathbf { M x } = \mathbf { v } _ { 1 } + \mathbf { v } _ { 2 }\).
The set of elements of \(\mathbb { R } ^ { 4 }\) which are not solutions of \(\mathbf { M x } = \mathbf { v } _ { 1 } + \mathbf { v } _ { 2 }\) is denoted by \(W\). - State, with a reason, whether \(W\) is a vector space.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.