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Q.

If the system of equations
(λ1)x+(λ4)y+λz=5λx+(λ1)y+(λ4)z=7(λ+1)x+(λ+2)y(λ+2)z=9
has infinitely many solutions, then λ2λ is equal

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a

12

b

10

c

20

d

6

answer is B.

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Detailed Solution

(λ1)x+(λ4)y+λz=5λx+(λ1)y+(λ4)z=7(λ+1)x+(λ+2)y(λ+2)z=9
For infinitely many solutions
D=λ1λ4λλλ1λ4λ+1λ+2(λ+2)=0(λ3)(2λ+1)=0Dx=5λ4λ7λ1λ49λ+2(λ+2)=02(3λ)(232λ)=0λ=3λ2+λ=9+3=12

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