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  • Can someone help me with this, - Mathematical Modelling - BITSAT-2

The value of \lambda and \mu for which the system of equations x+y+z=6, x+2y+3z=10 and x+2y+\lambdaz=\mu have no solution are: 

  • Option 1)

    \lambda= 3,\: \: \mu=10

  • Option 2)

    \lambda= 3,\: \: \mu \neq10

  • Option 3)

    \lambda \neq 3,\: \: \mu=10

  • Option 4)

    \lambda \neq 3,\: \: \mu \neq10

 

Answers (1)

best_answer

for no solution D=0 and at least 

one of D1,D2,D3 is non Zero 

So that according to question \begin{vmatrix} 1 & 1 &1 \\ 1& 2 &3 \\ 1 & 2 & \lambda \end{vmatrix}=0\:\: and \begin{vmatrix} 1 &1 &6 \\ 2&3 &10 \\ 2 &\lambda &\mu \end{vmatrix}\neq 0

\therefore \lambda =3\: and \mu \neq 10


Option 1)

\lambda= 3,\: \: \mu=10

This solution is incorrect 

Option 2)

\lambda= 3,\: \: \mu \neq10

This solution is correct 

Option 3)

\lambda \neq 3,\: \: \mu=10

This solution is incorrect 

Option 4)

\lambda \neq 3,\: \: \mu \neq10

This solution is incorrect 

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