Eigenvalues · Hard problem

A matrix $A = \begin{pmatrix}5 & 1 & -1\\0 & 3 & 2\\1 & -1 & 4\end{pmatrix}$ models a coupled system whose eigenvalues cannot easily be found by hand. Using Gershgorin's circle theorem (every eigenvalue lies within some row's disk, centered at that row's diagonal entry with radius the sum of the absolute values of the other entries in that row), find the smallest bound $B$ guaranteed by the theorem such that every eigenvalue $\lambda$ of $A$ satisfies $|\lambda| \le B$.