Matrices and Determinants: JEE Main 2020 Mathematics question

The sum of distinct values of $\lambda$ for which the system of equations $\left( {\lambda - 1} \right)x + \left( {3\lambda + 1} \right)y + 2\lambda z = 0$ $\left( {\lambda - 1} \right)x + \left( {4\lambda - 2} \right)y + \left( {\lambda + 3} \right)z = 0$ $2x + \left( {3\lambda + 1} \right)y + 3\left( {\lambda - 1} \right)z = 0$ has non-zero solutions, is ________ .