Question

Sol. [Key Concept: Infinitely many solutions $\Rightarrow \ D = D_{1} = D_{2} = D_{3} = 0$; solve for $\lambda$ and $\mu$.]

$${D = \lambda - 5 }{D_{1} = \lambda + \mu - 18 }{D_{2} = 4\lambda - 2\mu + 6 }{D_{3} = \mu - 13 }$$Here $x = \frac{D_{1}}{D};y = \frac{D_{2}}{D};z = \frac{D_{3}}{D}$

For infinitely many solutions

$${D = D_{1} = D_{2} = D_{3} = 0 }{\Rightarrow \lambda = 5;\mu = 13 }{\therefore\lambda + \mu = 18}$$