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Omni-MATH / In what case does the system of equations

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problem

In what case does the system of equations $\begin{matrix} x + y + mz = a \\ x + my + z = b \\ mx + y + z = c \end{matrix}$ have a solution? Find conditions under which the unique solution of the above system is an arithmetic progression.
Plain-text mathematical notation (without MathML)
In what case does the system of equations

$\begin{matrix} x + y + mz = a \\ x + my + z = b \\ mx + y + z = c \end{matrix}$

have a solution? Find conditions under which the unique solution of the above system is an arithmetic progression.
Original LaTeX notation
In what case does the system of equations

$\begin{matrix} x + y + mz = a \\ x + my + z = b \\ mx + y + z = c \end{matrix}$

have a solution? Find conditions under which the unique solution of the above system is an arithmetic progression.

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