Ask Questions, Get Answers

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

Find the value of $\lambda$ for which the set of equations $x+y-2z=0$, $2x-3y+z=0$, $x-5y+4z=\lambda$ are consistent.

(A) $\;\lambda=1$ (B) $\;\lambda=0$ (C) $\;\lambda=3$ (D) $\;\lambda=2$

Can you answer this question?

1 Answer

0 votes
A non-homogenous system has unique solution if $D\neq 0$ and infinite solutions if $D=D_1=D_2=D_3=0$
Now $D=\begin{vmatrix}1 &1 &-2\\2 &-3&1\\1 &-5&4\end{vmatrix}$$=0$
Hence $D_1,D_2,D_3$ should all be zero.i.e $D_1=0$
$\Rightarrow D_1=\begin{vmatrix}0 &1&-2\\0 &-3&1\\\lambda &5&4\end{vmatrix}=0$
$\Rightarrow \lambda(1-6)=0$
Hence (b) is the correct answer.
answered Nov 19, 2013 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