EMLA Q.48
0. For which value of k, the following system is consistent?
2x-5ky+6z=0
kx+2y-2z=0
2x+2y-kz=0
- Option : B
- Explanation :
Equations are consistent, if rank of A and that of k are equal. But in this case it is always true. Hence the equations
will have a trivial solution if IAI 0
Therefore only non- trivial solution will exist if IAI = 0
2(-2k+4) + k(-k2+4+6)(2k-4) = 0
-5k3+ 20k - 4k + 8 + 12k - 24 = 0
5k3 - 28k + 16 = 0
5k3 - 10k2 + 10k2 - 20k - 8k + 16 = 0
(5k2+ 10k - 8)(k - 2) = 0
or 2
or 2
0
-5k3+ 20k - 4k + 8 + 12k - 24 = 0
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