જો સુરેખ રેખાઓની સહંતિ x-2 y+z=-4 &nbs | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\mathrm{D}=\left|\begin{array}{ccc}1 & -2 & 1 \ 2 & \alpha & 3 \ 3 & -1 & \beta\end{array}ight|$

$=1(\alpha \beta+3)+2

Vedclass · Accepted Answer

$58$

Vedclass · Answer

$\mathrm{D}=\left|\begin{array}{ccc}1 & -2 & 1 \ 2 & \alpha & 3 \ 3 & -1 & \beta\end{array}ight|$

$=1(\alpha \beta+3)+2(2 \beta-9)+1(-2-3 \alpha)$

$=\alpha \beta+3+4 \beta-18-2-3 \alpha$

For infinite solutions $\mathrm{D}=0, \mathrm{D}_1=0, \mathrm{D}_2=0$ and

$D_3=0$

 $D=0$

 $\alpha \beta-3 \alpha+4 \beta=17 \ldots....($1$)$

$D_1=\left|\begin{array}{ccc}-4 & -2 & 1 \ 5 & \alpha & 3 \ 3 & -1 & \beta\end{array}ight|=0$

$D_2=\left|\begin{array}{ccc}1 & -4 & 1 \ 2 & 5 & 3 \ 3 & 3 & \beta\end{array}ight|=0$

$\Rightarrow 1(5 \beta-9)+4(2 \beta-9)+1(6-15)=0$

$13 \beta-9-36-9=0$

$13 \beta=54, \beta=\frac{54}{13} 	ext { put in }(1)$

$\frac{54}{13} \alpha-3 \alpha+4\left(\frac{54}{13}ight)=17$

$54 \alpha-39 \alpha+216=221$

$15 \alpha=5 \quad \alpha=\frac{1}{3}$

$	ext { Now, } 12 \alpha+13 \beta=12 \cdot \frac{1}{3}+13 \cdot \frac{54}{13}$

$=4+54=58$

જો સુરેખ રેખાઓની સહંતિ $x-2 y+z=-4 $ ; $2 x+\alpha y+3 z=5 $ ; $3 x-y+\beta z=3$ ને અનંત ઉકેલ હોય તો $12 \alpha+13 \beta$ ની કિમંત મેળવો.

Similar Questions

$\Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right|$ નું મૂલ્ય શોધો.

$m$ ની કેટલી કિમંતો માટે રેખાઓ $x + y - 1 = 0$, $(m - 1) x + (m^2 - 7) y - 5 = 0 \,\,\&\,\, (m - 2) x + (2m - 5) y = 0$ ઓ સંગામી થાય.

નિશ્ચાયકની કિમત મેળવો : $\left|\begin{array}{ccc}
3 & -4 & 5 \\
1 & 1 & -2 \\
2 & 3 & 1
\end{array}\right|$

$\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ - a}&1&c\\{ - b}&{ - c}&1\end{array}\,} \right| = $

જો $\left| {\,\begin{array}{*{20}{c}}5&3&{ - 1}\\{ - 7}&x&{ - 3}\\9&6&{ - 2}\end{array}\,} \right| = 0$, તો $ x$ મેળવો.