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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 indefinitely many solutions. Then $\lambda $ is a root of the quadratic equation

• ✓
  ${\lambda ^2} - \lambda  - 6\, = 0$
• B
  ${\lambda ^2} - 3\lambda  - 4 = 0$
• C
  ${\lambda ^2} + 3\lambda  - 4 = 0$
• D
  ${\lambda ^2} + \lambda  - 6 = 0$