Given that the matrix $A$ has eigenvalues $\lambda_1 = 8$ with corresponding eigenvector $\vec{v}_{1} = \left[\begin{array}{c} -1\cr 1 \end{array}\right]$ and $\lambda_2 = 1$ with corresponding eigenvector $\vec{v}_{2} = \left[\begin{array}{c} 2\cr -1 \end{array}\right]$, find $A$.

$A=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$