The system of equations 3x−y+4z=3, x+2y−3z=−2, 6x+5y+λz=−3 has atleast one solution when

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λ=−5

λ=3

λ=5

λ=6

answer is A.

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Detailed Solution

Augmented matrix =3−14312−3−265λ−33R2−R1R3−2R1~3−14307−13−907λ−8−9R3−R23−14307−13−900λ+50 The system of equations has atleast on solution ⇒λ+5=0⇒λ=−5

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