Question

If the system of equations
$x+y+z=6$
$x + 2y+3z= 10$
$x + 2y+\lambda z=0$
has a unique solution, then $\lambda$ is not equal to

• A. $1$
• B. $0$
• C. $2$
• D. $3$

Answer 1

Answer: (D)

Given system of equations is
$x+y+z=6$
$x+2y+3z= 10$
$x + 2y+\lambda z=0$
It has unique solution.
$\therefore \begin{vmatrix}1&1&1\\ 1&2&3\\ 1&2&\lambda\end{vmatrix}\ne0$
$\Rightarrow 1\left(2\lambda-6\right)-1\left(\lambda-3\right)+1\left(2-2\right)\ne0$
$\Rightarrow 2\lambda-6-\lambda+3\ne0 \Rightarrow \lambda-3\ne0 \Rightarrow \lambda\ne3$