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The value of \lambda \; \; and\; \; \mu for which the system of linear eq  x+y+z=2, x+2y+3z=5, x+3y+\lambda z = \mu has infinitely many solutions are respectively ..
 
Option: 1 5 & 8   
Option: 2 4 & 9   
Option: 3 6 & 8     
Option: 4 5 & 2

Answers (1)

best_answer

\\x+y+z=2 \\ x+2 y+3 z=5 \\ x+3 y+\lambda z=\mu

\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda \end{array}\right|=0\Rightarrow\lambda=5

and

\left|\begin{array}{lll} 1 & 1 & 2 \\ 1 & 2 & 5 \\ 1 & 3 & \mu \end{array}\right|=0\Rightarrow\mu=8

Correct Answer : Option A

Posted by

himanshu.meshram

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