Question

Given $2x-y+2z=2,x-2y+z=-4$ and $x+y+\lambda z=4$ then the value of $\lambda$ such that the given system of equations has no solution is

• A. $3$
• B. $1$
• C. $0$
• D. $-3$

Answer 1

The correct option is B $1$

Given that the system of equation has no solution. Given equations are

$2x-y+2z=2,x-2y+z=-4,x+y+\lambda z=4$

It will have no solution when $A=0$

$A=\left|\begin{array}{ccc}2& -1& 2\\ 1& -2& 1\\ 1& 1& \lambda \end{array}\right|=0$

Apply $c_2\to c_1+2c_2$ and $c_3\to c_1-c_3$

So $A=\left|\begin{array}{ccc}2& 0& 0\\ 1& -3& 0\\ 1& 3& 1-\lambda \end{array}\right|=0$

Solve it to get $1-\lambda =0\Rightarrow \lambda =1$