Question
Solve the following equations by inversion method $:2x + 6y = 8, x + 3y = 5$
✓
Answer
The given equations can be written in the matrix form as $:\left[\begin{array}{ll}2 & 6 \\ 1 & 3\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}8 \\ 5\end{array}\right]$
This is of the form $AX = B,$ where
$\mathrm{A}=\left[\begin{array}{ll}2 & 6 \\ 1 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}x \\ y\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}8 \\ 5\end{array}\right]$
Let us find $A^{-1}.$
$|A|=\left|\begin{array}{ll}2 & 6 \\ 1 & 3\end{array}\right|=6-6=0$
$\therefore A^{-1}$ does not exist.
Hence, $x$ and $y$ do not exist.
This is of the form $AX = B,$ where
$\mathrm{A}=\left[\begin{array}{ll}2 & 6 \\ 1 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}x \\ y\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}8 \\ 5\end{array}\right]$
Let us find $A^{-1}.$
$|A|=\left|\begin{array}{ll}2 & 6 \\ 1 & 3\end{array}\right|=6-6=0$
$\therefore A^{-1}$ does not exist.
Hence, $x$ and $y$ do not exist.
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