The system of equations [aligned & x+y+z=6, & x+2 y+5 z=9, & x+5 y+ z=, aligned] has no so…

Question

The system of equations

$$\begin{aligned}
& x+y+z=6, \
& x+2 y+5 z=9, \
& x+5 y+\lambda z=\mu,
\end{aligned}$$

has no solution if

Accepted Answer

$$\begin{aligned}
& \mathrm{D}=\left|\[\begin{array}{lll} 1 & 1 & 1 \ 1 & 2 & 5 \ 1 & 5 & \lambda \end{array}\end{aligned}$$\right|=0 \
\& \lambda=17 \
\& D\_z=\left|$$\begin{array}{lll} 1 & 1 & 6 \ 1 & 2 & 9 \ 1 & 5 & \mu \end{array}$$\right| \neq 0 \
\& \mu \neq 18
\]

Solutions · 1