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Let λ be a real number for which the system of linear equations x + y + x = 6, 4x + λ y – λ z = λ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then λ is a root of the quadratic equation:

1. λ 2 + λ – 6 = 0
2. λ 2 – λ – 6 = 0
3. λ 2 – 3 λ – 4 = 0
4. λ 2 + 3 λ – 4 = 0

Correct answer: λ 2 – λ – 6 = 0

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