Question

The value of $\lambda$, such that the following system of equations $2x - y - 2z = 2$; $x - 2y + z = -4$; $x + y + \lambda z = 4$ has no solution, is

• A. 3
• B. 1
• C. 0
• D. -3

Answer 1

Answer: (B)

1

Answer 2

The correct answer is B:1
Given that:
The system of equation has no solution for a value of $\lambda$
The equation is;
$2x-y+2z=2$
$x-2y+z=-4$
$x+y+\lambda=4$
as the system of equation has no solution
$\therefore$ A=0
$\begin{vmatrix}2&-1&-2\\\ 1&-2&1\\\ 1&1&\lambda\end{vmatrix}=0$
Applying $C_2\rightarrow C_1+2C_2 \space{and}\space C_3\rightarrow C_1-C_3$
we have $A=\begin{vmatrix}2&0&0\\\1&-3&0\\\1&3&(1-\lambda)\end{vmatrix}=0$
$\therefore$ $1-\lambda=0$
⇒$\lambda=1$