Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Determinants
0 votes

The values of $\lambda$ and $\mu$ for which the equations $x+y+z=3,x+3y+2z=6,x+\lambda y+3z=\mu$ have

$\begin{array}{1 1}(A)\;\text{a unique solution if }\lambda=5\;\mu \in R&(B)\;\text{no solution if }\lambda\neq 5,\mu=9\\(C)\;\text{Infinite many solution if }\lambda=5,\mu\neq 9&(D)\;\text{None of the above}\end{array}$

Can you answer this question?

1 Answer

0 votes
Given :
$\Rightarrow$ If $\Delta\neq 0$ (i.e) $\lambda\neq 0$ the solution is unique.
Case-I:If $\lambda\neq 5$ and $\mu$ any real number gives unique solution.
Case-II:If $\lambda=5\Rightarrow \Delta =0$
$\Delta_2=\begin{vmatrix}1&3&1\\1&6&2\\1&\mu&3\end{vmatrix}=-\mu +9$
If $\Delta\neq 0,\mu\neq 9$.The system has no solution.
Case III:If $\lambda=5$ and $\mu=9$ equation has infinite solution.
Hence (D) is the correct answer.
answered Apr 25, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App