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Maths-

General

Easy

Question

The value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

3
-3
2
-2

The correct answer is: -2

The question is as follows the value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution, as we know for no solution case determinant of coefficients is equal to 0

The given equations are
2x-y-z=12
x-2y+z=-4
x+y+λz=4
Their determinant =D
For no solution case D=0
$open vertical bar table row 2 cell negative 1 end cell cell negative 1 end cell row 1 cell negative 2 end cell 1 row 1 1 lambda end table close vertical bar equals 0$
=> 2(−2λ−1)+1(λ−1)−1(1+2)=0
=> −3λ−6=0
λ=−2

Hence λ=−2 for no solution.

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Hence option B is the correct option

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Hence option B is the correct option

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Statement‐II : The inverse of singular matrix does not exist.

Hence option D is the suitable option

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