Consider the matrix recurrence $\vec{v}_n = A\vec{v}_{n-1}$ where $A = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$ and $\vec{v}_0 = \begin{pmatrix} 1 \\ 0 \end{pmatrix}$. What is the first component of $\vec{v}_3$?