Algebra 2SuperchallengeLinear Systems & Matrices

Linear Systems & Matrices · Superchallenge problem

Consider the system

\begin{aligned} x + y + kz &= 1 \\ x + ky + z &= k \\ kx + y + z &= k^2. \end{aligned}

Find the sum of all real values of $k$ for which the system does not have exactly one solution.