Question

The value of $\lambda$ and$\mu$ for which the simultaneous equation
$x+y+z=6$, $x+2y+3z=10$ and $x+2y+\lambda z=\mu$ have a unique solution are

• A. $\lambda \ne 2$
• B. $\mu =3$
• C. $\lambda =3$ and $\mu =3$
• D. $\lambda \ne 3$

Answer 1

The correct option is D $\lambda \ne 3$

For unique solution, $\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 2& \lambda \end{array}\right|\ne 0$
$\Rightarrow 1(2\lambda -6)-1(\lambda -3)+1(2-2)\ne 0$
$\Rightarrow \lambda \ne 3$