સુરેખ સમીકરણ સંહિતા

(lambda-1) x+(3 | vedclass

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Question

$(\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0$

$(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0$

$2 x+(3 \lambda+1) y+(3 \lambda-3) z=0$

$\left|

Vedclass · Accepted Answer

$3$

Vedclass · Answer

$(\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0$

$(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0$

$2 x+(3 \lambda+1) y+(3 \lambda-3) z=0$

$\left|\begin{array}{ccc}\lambda-1 & 3 \lambda+1 & 2 \lambda \ \lambda-1 & 4 \lambda-2 & \lambda+3 \ 2 & 3 \lambda+1 & 3 \lambda-3\end{array}ight|=0$

$R _{1} ightarrow R _{1}- R _{2}$ and $R _{2} ightarrow R _{2}- R _{3}$

$\left|\begin{array}{ccc}0 & 3-\lambda & \lambda-3 \ \lambda-3 & \lambda-3 & -2(\lambda-3) \ 2 & 3 \lambda+1 & 3 \lambda-3\end{array}ight|=0$

$(\lambda-3)^{2}\left|\begin{array}{ccc}0 & -1 & 1 \ 1 & 1 & -2 \ 2 & 3 \lambda+1 & 3 \lambda-3\end{array}ight|=0$

$(\lambda-3)^{2}[(3 \lambda+1)+(3 \lambda-1)]=0$

$6 \lambda(\lambda-3)^{2}=0 \Rightarrow \lambda=0,3$

$\operatorname{Sum}=3$

Similar Questions

ધન સંખ્યાઓ $x,y$ અને $z$ માટે નિશ્રાયક $\left| {\,\begin{array}{*{20}{c}}1&{{{\log }_x}y}&{{{\log }_x}z}\\{{{\log }_y}x}&1&{{{\log }_y}z}\\{{{\log }_z}x}&{{{\log }_z}y}&1\end{array}\,} \right|$ ની કિમત મેળવો.

સુરેખ સમીકરણ સંહતિ $3 x-2 y-k z=10$ ; $2 x-4 y-2 z=6$ ; $x+2 y-z=5\, m$ સુસંગત ન હોય તો

$\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right| \ne . . . .$

$\left| {\,\begin{array}{*{20}{c}}2&8&4\\{ - 5}&6&{ - 10}\\1&7&2\end{array}\,} \right|$ = . . ..

જો $\left| \begin{gathered}
- 6\ \ \,\,1\ \ \,\,\lambda \ \ \hfill \\
\,0\ \ \,\,\,\,3\ \ \,\,7\ \ \hfill \\
- 1\ \ \,\,0\ \ \,\,5\ \ \hfill \\
\end{gathered} \right| = 5948 $, તો $\lambda $ મેળવો.