Given a0=1,a1=2,a2=7,a3=20a_0 = 1, a_1 = 2, a_2 = 7, a_3 = 20a0=1,a1=2,a2=7,a3=20, and assuming an=c1an−1+c2an−2a_n = c_1 a_{n-1} + c_2 a_{n-2}an=c1an−1+c2an−2 for n≥2n \geq 2n≥2, which system of equations determines c1c_1c1 and c2c_2c2?
{7=2c1+1c220=7c1+2c2\begin{cases} 7 = 2c_1 + 1c_2 \\ 20 = 7c_1 + 2c_2 \end{cases}{7=2c1+1c220=7c1+2c2
{2=c17=2c1+c2\begin{cases} 2 = c_1 \\ 7 = 2c_1 + c_2 \end{cases}{2=c17=2c1+c2
{c1+c2=92c1−c2=5\begin{cases} c_1 + c_2 = 9 \\ 2c_1 - c_2 = 5 \end{cases}{c1+c2=92c1−c2=5
{1=c1+c22=2c1+c2\begin{cases} 1 = c_1 + c_2 \\ 2 = 2c_1 + c_2 \end{cases}{1=c1+c22=2c1+c2