Q.

If λbe a real number of which the system of linear equations x+y+z=6,4x+λy−λz=λ−2,3x+2y−4z=−5 has infinitly many solutions. Then λis a root of the equation

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a

λ2+λ−6=0

b

λ2+3λ−4=0

c

λ2−3λ−4=0

d

λ2−λ−6=0

answer is D.

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Detailed Solution

x+y+z=6----(1)4x+λy−λz=λ−2----(2)3x+2y−4z=−5------(3)(1)+(3) = (2) satisfy forλ =3which is a root of λ2−λ−6=0
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If λbe a real number of which the system of linear equations x+y+z=6,4x+λy−λz=λ−2,3x+2y−4z=−5 has infinitly many solutions. Then λis a root of the equation