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Let $\lambda$ be a real number for which the system of linear equations: $x + y + z = 6$, $4x + \lambda y - \lambda z = \lambda - 2$, $3x + 2y - 4z = -5$ has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation:
(1) $\lambda^2 + 3\lambda - 4 = 0$
(2) $\lambda^2 - 3\lambda - 4 = 0$
(3) $\lambda^2 + \lambda - 6 = 0$
(4) $\lambda^2 - \lambda - 6 = 0$
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