= Solution
{c}
For $A+\gamma B$ with $\gamma\geq0$, the three <Gershgorin discs> have positive real centres $a+\gamma$, $2c+2\gamma$, $6b+6\gamma$, and radii $b+c$, $a+b+\gamma$, $a+c+\gamma$. Centre minus radius is respectively
$$
a-b-c+\gamma>0,\qquad2c-a-b+\gamma>0,\qquad6b-a-c+5\gamma>0.
$$
Thus none of the discs contains zero. By the <Gershgorin circle theorem>, zero is not an <eigenvalue>, so $A+\gamma B$ is nonsingular for every $\gamma\geq0$. Consequently
$$
\boxed{\Gamma=\varnothing.}
$$
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