Question

If the system of equations 2x - y - z = 12, x - 2y + z = -4, x + y + λz = 4 has no solution, then λ = ________________.

Answer 1

The given system of equations 2x − y − z = 12, x − 2y + z = −4 and x + y + λz = 4 has no solution.

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

$\Rightarrow 2\left(-2\lambda -1\right)-\left(-1\right)\left(\lambda -1\right)-1\left(1+2\right)=0$

$\Rightarrow -4\lambda -2+\lambda -1-3=0$

$\Rightarrow -3\lambda -6=0$

$\Rightarrow -3\lambda =6$

$\Rightarrow \lambda =-2$

Thus, the value of λ = −2.

If the system of equations 2x − y − z = 12, x − 2y + z = −4, x + y + λz = 4 has no solution, then λ = ___−2___.