$$A=\left[\begin{array}{cccc} 1 & a & a^{2} & a^{3} \\ a^{3} & 1 & a & a^{2} \\ a^{2} & a^{3} & 1 & a \\ a & a^{2} & a^{3} & 1 \end{array}\right], \quad b=\left[\begin{array}{l} \gamma \\ 0 \\ 0 \\ 0 \end{array}\right], \quad \gamma=1-a^{4} \neq 0$$

Find the LU factorization of the matrix $A$ and use it to solve the system $A x=b$ via forward and backward substitution. [Other methods of solution are not acceptable.]