Mathematics

Mathematics

Problem

Let λ\lambda be a real number for which the system of linear equations x+y+z=6x + y + z = 6, 4x+λy−λz=λ−24x + \lambda y - \lambda z = \lambda - 2, 3x+2y−4z=−53x + 2y - 4z = -5 has infinitely many solutions. Then λ\lambda is a root of the quadratic equation. (1) λ2−3λ−4=0\lambda^2 - 3\lambda - 4 = 0 (2) λ2−λ−6=0\lambda^2 - \lambda - 6 = 0 (3) λ2+3λ−4=0\lambda^2 + 3\lambda - 4 = 0 (4) λ2+λ−6=0\lambda^2 + \lambda - 6 = 0

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