11 Find the rank of the matrix \(\mathbf { A }\), where $$\mathbf { A } = \left( \begin{array} { r r r r } 1 & 1 & 2 & 3
4 & 3 & 5 & 16
6 & 6 & 13 & 13
14 & 12 & 23 & 45 \end{array} \right)$$ Find vectors \(\mathbf { x } _ { 0 }\) and \(\mathbf { e }\) such that any solution of the equation $$\mathbf { A x } = \left( \begin{array} { r } 0
2
- 1
3 \end{array} \right)$$ can be expressed in the form \(\mathbf { x } _ { 0 } + \lambda \mathbf { e }\), where \(\lambda \in \mathbb { R }\). Hence show that there is no vector which satisfies (*) and has all its elements positive.