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