Question 381 of 472MediumMCQ
Let the system of linear equations
4x + \[\lambda\]y + 2z = 0
2x - y + z = 0
\[\mu\]x + 2y + 3z = 0, \[\lambda\], \[\mu\] ∈ Solutions · 1
Official solution
Given, system of linear equations
4x + \[\lambda\]y + 2z = 0
2x - y + z = 0
\[\mu\]x + 2y + 3z = 0
For non-trivial solution, \[\Delta\] = 0
\[\left| {42μλ−12213 } \right| = 0\]
\[ \Rightarrow 4( - 3 - 2) - \lambda (6 - \mu ) + 2(4 + \mu ) = 0\]
\[ \Rightarrow - \lambda (6 - \mu ) - 2(6 - \mu ) = 0\]
\[ \Rightarrow (6 - \mu )(\lambda + 2) = 0\]
\[ \Rightarrow \lambda = - 2\] and \[\mu \in R\] or \[\mu\] = 6 and \[\lambda \in R\]. Answer the question to unlock