Key Concept: A system of linear equations is said to be homogeneous if all the constant terms are zero. For a homogeneous system of linear equations of the form $AX = 0$, where $A$ is the coefficient matrix, $X$ is the column vector of variables, and $0$ is the zero vector, it has:

1. Trivial solution (x=y=z=0) if and only if $\det(A) \neq 0$.
2. Non-trivial solutions (at least one of x, y, z is non-zero) if and only if $\det(A) = 0$.

The problem asks for the values of $\lambda$ for which the given system has non-trivial solutions, which means