સુરેખ સમીકરણોની સંહતિનો ઉકેલ શ્રેણિકના ઉપયોગથી મેળવો : 4 x-3 y=3 ; 3 x-5 y=7

Q: સુરેખ સમીકરણોની સંહતિનો ઉકેલ શ્રેણિકના ઉપયોગથી મેળવો : $4 x-3 y=3 ; 3 x-5 y=7$

The given system of equation can be written in the form of $A X=B$, where$A=\left[\begin{array}{ll}4 & -3 \\ 3 & -5\end{array}\right], X=\left[\begin{array}{l}x \\ y\end{array}\right]$ and $B=\left[\begin{array}{l}3 \\ 7\end{array}\right]$ Now, $|A|=-20+9=-11 \neq 0$ Thus, $A$ is non-singular. Therefore, its inverse exists. Now, $A^{-1}=\frac{1}{|A|}(a d j A)=-\frac{1}{11}\left[\begin{array}{ll}-5 & 3 \\-3 & 4\end{array}\right]=\frac{1}{11}\left[\begin{array}{ll}5 & -3 \\3 & -4\end{array}\right]$ $\therefore X=A^{-1} B=\frac{1}{11}\left[\begin{array}{ll}5 & -3 \\ 3 & -4\end{array}\right]\left[\begin{array}{l}3 \\ 7\end{array}\right]$ $\Rightarrow\left[\begin{array}{l}x \\ y\end{array}\right]=\frac{1}{11}\left[\begin{array}{ll}5 & -3 \\ 3 & -4\end{array}\right]\left[\begin{array}{l}3 \\ 7\end{array}\right]$ $=\frac{1}{11}\left[\begin{array}{c}15-21 \\ 9-28\end{array}\right]$ $=\frac{1}{11}\left[\begin{array}{l}-6 \\ -19\end{array}\right]$ $=\left[\begin{array}{r}-\frac{6}{11} \\ -\frac{19}{11}\end{array}\right]$ Hence, $x=\frac{-6}{11}$ and $y=\frac{-19}{11}$

MCQ

ગુજરાતી માધ્યમ

સુરેખ સમીકરણોની સંહતિનો ઉકેલ શ્રેણિકના ઉપયોગથી મેળવો : $4 x-3 y=3 ; 3 x-5 y=7$

A$x=\frac{6}{11},y=\frac{-19}{11}$
B$x=\frac{-6}{11},y=\frac{19}{11}$
C$x=\frac{6}{11},y=\frac{19}{11}$
D$x=\frac{-6}{11},y=\frac{-19}{11}$

Medium

ધોરણ 12 સાયન્સ
ગણિત
3 and 4 . determinant and metrices
JEE

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