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  4. For what value of λ , the system of equations x+y+z=6, text x+2y+3z=10, x+2y+λ z=10 is consistent?

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Q. For what value of $ \lambda , $ the system of equations $ x+y+z=6,\text{ }x+2y+3z=10, $ $ x+2y+\lambda z=10 $ is consistent?

KEAMKEAM 2003

Solution:

The system of equations is consistent, if $ \left| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 2 & \lambda \\ \end{matrix} \right|=0 $ $ \Rightarrow $ $ \lambda =3 $