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

The Correct Option is B

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 \(A=\begin{vmatrix}2&0&0\\1&-3&0\\1&3&(1-\lambda)\end{vmatrix}=0\)
\(\therefore\) \(1-\lambda=0\)
⇒\(\lambda=1\)