For which $a$ does the system of linear equations have a root Choose a possible $a$ such that the linear equations have a root
$$\begin{matrix} x+2y+3z=a \\
                 4x+5y+6z=a^2 \\
                 7x+8y+9z=a^3 \end{matrix}$$
Do I begin by finding the possible values of $a$ such that the system is consistent?

Then first equation plus the third equation minus twice the second yields $a^3-2a^2+a=a(a-1)^2=0$.
