Define the four vectors in $\mathbb{R}^4$ by
$v_1=\left( \begin{array}{ccc} 1 \\ 0 \\ 0 \\ 0 \end{array} \right), v_2=\left( \begin{array}{ccc} 1 \\ 1 \\ 0 \\ 0 \end{array} \right), v_3=\left( \begin{array}{ccc} 1 \\ 1 \\ 1 \\ 0 \end{array} \right), v_4=\left( \begin{array}{ccc} 1 \\ 1 \\ 1 \\ 1 \end{array} \right). $
I'm now asked to find the basis dual to $\{v_1,v_2,v_3,v_4 \}$ in $\mathbb{R}^4$, wth each vector expressed as a linear combination of the standard basis in $\mathbb{R}^4$.
Now, this is one of those situations where I 'know' all of the bookwork regarding dual bases etc. however, what seems like a simple application presents quite a hurdle.
Any explanation of how to progress would be very appreciated.