P $4\mathrm{.}4-1o+$ The voltages $v_a,v_b,$ and $v_c$ in Figure P $4\mathrm{.}4-1$ are the node voltages corresponding to nodes $a,b,$ and $c.$ The values of these voltages are:

$v_a=8\mathrm{.}667V,v_b=2V,$ and $v_c=10V$

Determine the value of $A,$ the gain of the dependent source.