The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + λz = μ,

Question

The system of equations

x + y + z = 6,

x + 2y + 5z = 9,

\(x + 5y+\lambda z=\mu,\)

has no solution if

(1) \(\lambda=17, \mu \neq 18\)

(2) \(\lambda \neq 17, \mu \neq 18\)

(3) \(\lambda=15, \mu \neq 17\)

(4) \(\lambda=17, \mu=18\)
 

Answer 1

Correct option is (1) \(\lambda=17, \mu \neq 18\)   

\(D=\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 5 \\ 1 & 5 & \lambda\end{array}\right|=0\)

\(\lambda=17\)

\(D_{z}=\left|\begin{array}{ccc}1 & 1 & 6 \\ 1 & 2 & 9 \\ 1 & 5 & \mu\end{array}\right| \neq 0\)

\(\mu \neq 18\)