Let the system of linear equations
4x + $\lambda$y + 2z = 0
2x $-$ y + z = 0
$\mu$x + 2y + 3z = 0, $\lambda$, $\mu$$\in$R.
has a non-trivial solution. Then which of the following is true?
Solution
<p>Given, system of linear equations</p>
<p>4x + $\lambda$y + 2z = 0</p>
<p>2x $-$ y + z = 0</p>
<p>$\mu$x + 2y + 3z = 0</p>
<p>For non-trivial solution, $\Delta$ = 0</p>
<p>$$\left| {\matrix{
4 & \lambda & 2 \cr
2 & { - 1} & 1 \cr
\mu & 2 & 3 \cr
} } \right| = 0$$</p>
<p>$\Rightarrow 4( - 3 - 2) - \lambda (6 - \mu ) + 2(4 + \mu ) = 0$</p>
<p>$\Rightarrow - \lambda (6 - \mu ) - 2(6 - \mu ) = 0$</p>
<p>$\Rightarrow (6 - \mu )(\lambda + 2) = 0$</p>
<p>$\Rightarrow \lambda = - 2$ and $\mu \in R$ or $\mu$ = 6 and $\lambda \in R$.</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
This question is part of PrepWiser's free JEE Main question bank. 274 more solved questions on Matrices and Determinants are available — start with the harder ones if your accuracy is >70%.