Gershgorin exclusion for a matrix-pencil parameter

To exclude zero as an eigenvalue of $A+sB$, it is enough that every row has positive real diagonal entry exceeding the sum of the absolute values of its off-diagonal entries. All Gershgorin discs then lie strictly in the right half-plane. Forthe three diagonal-dominance margins of $A+sB$ are $2s,2+s,s$, all positive for $s>0$. Thus $A-\mu B$ is nonsingular for negative real $\mu$. Working with the pencil directly avoids computing either a determinant polynomial or $B^{-1}A$.