Question

Solve by matrix inversion method $2x-y=7;3x-2y=11$

Answer 1

The given set of equations can be represented in matrix form as $AX=B$ , where $A=\left[\begin{array}{cc}2& -1\\ 3& -2\end{array}\right]$ and $B=\left[\begin{array}{c}7\\ 11\end{array}\right]$

Therefore we get $X=A^{-1}B$

$A^{-1}=-1\times \left[\begin{array}{cc}-2& 1\\ -3& 2\end{array}\right]=\left[\begin{array}{cc}2& -1\\ 3& -2\end{array}\right]$

$X=\left[\begin{array}{cc}2& -1\\ 3& -2\end{array}\right]\left[\begin{array}{c}7\\ 11\end{array}\right]=\left[\begin{array}{c}3\\ -1\end{array}\right]$

Therefore $x=3$ and $y=-1$