Express the vectors e 1 ∗ , e 2 ∗ {\displaystyle {}e_{1}^{*},e_{2}^{*}} of the standard dual basis as linear combinations with respect to the dual basis u 1 ∗ , u 2 ∗ {\displaystyle {}u_{1}^{*},u_{2}^{*}} to the basis u 1 = ( 1 4 ) , u 2 = ( − 2 2 ) {\displaystyle {}u_{1}={\begin{pmatrix}1\\4\end{pmatrix}}\,,u_{2}={\begin{pmatrix}-2\\2\end{pmatrix}}} .
