JEE Main On 8 April 2017 Question 27
Question: The number of real values of $ \lambda $ for which the system of linear equations $ 2x+4y-\lambda z=0 $ $ 4x+\lambda y+2z=0 $ $ \lambda x+2y+2z=0 $ has infinitely many solutions, is : [JEE Online 08-04-2017]
Options:
A) 3
B) 1
C) 2
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \Delta =0 $ $ \begin{vmatrix} 2 & 4 & -\lambda \\ 4 & \lambda & z \\ \lambda & z & 2 \\ \end{vmatrix} \begin{vmatrix} 2 & 4 \\ 4 & \lambda =0 \\ \lambda & z \\ \end{vmatrix} $ $ =-(32+8-{{\lambda }^{3}})=0 $ $ =\lambda 3+4\lambda -40=0 $
