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# The value of 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 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

=> 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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