Question

lf the system of equations $x+y+z=6,x+2y+\lambda z=0,x+2y+3z=10$ has no solution,
then $\lambda$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

For no solution, the determinant formed by co-efficient of $x,$$y$ and $z$ has to be $0$
$\therefore \left|\begin{array}{ccc}1& 1& 1\\ 1& 2& \lambda \\ 1& 2& 3\end{array}\right|=0$

Using this property, if any two row or column are equal then value of determinant is $0$

$\therefore$ make $R_2=R_3$

Take $\lambda =3$

We get two rows are equal