The system of equations l x+y+z=6 x+2 y+5 z=9 x+5 y+ z= has no so… - Vidyadip

MCQ

The system of equations
$
\begin{array}{l}
x+y+z=6 \\
x+2 y+5 z=9 \\
x+5 y+\lambda z=\mu
\end{array}
$
has no solution if

✓
$\lambda=17, \mu \neq 18$
B
$\lambda \neq 17, \mu \neq 18$
C
$\lambda=15, \mu \neq 17$
D
$\lambda=17, \mu=18$

✓

Answer

Correct option: A.

$\lambda=17, \mu \neq 18$

(A)
$
\begin{array}{l}
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}{lll}
1 & 1 & 6 \\
1 & 2 & 9 \\
1 & 5 & \mu
\end{array}\right| \neq 0 \\
\mu \neq 18
\end{array}
$

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