\displaystyle V_A=V_1,\ V_B=V_A+3k\times\frac{V_A}{R_A}=\left(1+\frac{3k}{R_A}\right)V_1

\displaystyle \frac{V_1}{R_A}+\frac{V_B}{6k}=\frac{V_0-V_B}{12k}

\displaystyle \frac{V_1}{R_A}+\left(1+\frac{3k}{R_A}\right)\frac{V_1}{6k}=\frac{V_0}{12k}-\left(1+\frac{3k}{R_A}\right)\frac{V_1}{12k}

\displaystyle V_0=V_1\times\left(\frac{1}{R_A}+\left(1+\frac{3k}{R_A}\right)\frac{1}{4k}\right)\times12k

\displaystyle A=\frac{V_0}{V_1}=\frac{21k}{R_A}+3=10,\ R_A=3k\Omega