%%

Let the system of linear equations 4x + $$\lambda$$y + 2z = 0 2x $$-$$ y + z = 0 $$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R. has a non-trivial solution. Then which of the following is true?

JEE · Math · previous-year question

  1. A.$$\mu$$ = 6, $$\lambda$$$$\in$$Rcorrect
  2. B.$$\lambda$$ = 3, $$\mu$$$$\in$$R
  3. C.$$\mu$$ = $$-$$6, $$\lambda$$$$\in$$R
  4. D.$$\lambda$$ = 2, $$\mu$$$$\in$$R

Answer

A. $$\mu$$ = 6, $$\lambda$$$$\in$$R

Explanation

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 $$\left| {\begin{matrix} 4 & \lambda & 2 \\ 2 & { - 1} & 1 \\ \mu & 2 & 3 \\ \end{matrix} } \right| = 0$$ $$ \Rightarrow 4( - 3 - 2) - \lambda (6 - \mu ) + 2(4 + \mu ) = 0$$ $$ \Rightarrow - \lambda (6 - \mu ) - 2(6 - \mu ) = 0$$ $$ \Rightarrow (6 - \mu )(\lambda + 2) = 0$$ $$ \Rightarrow \lambda = - 2$$ and $$\mu \in R$$ or $$\mu$$ = 6 and $$\lambda \in R$$.

Practice more JEE questions

Answer thousands more real JEE previous-year questions free, get graded instantly, and climb the global ranked leaderboard.

Practice JEE free →

More JEE Math questions