Question

Solve system of linear equations, using matrix method.
2x-y=-2
3x+4y=3

Answer 1

The given system of equations can be written in the form of AX = B, where
A=$\begin{vmatrix} 2 &-1 \\\ 3& 4 \end{vmatrix}$, X=$\begin{vmatrix} x \\\ y \end{vmatrix}$and B=$\begin{vmatrix} -2 \\\ 3 \end{vmatrix}$
$Now |A|=8+3=11≠0$
Thus, A is non-singular. Therefore, its inverse exists.
Now,
A-1=$\frac{1}{|A|}$adjA=\frac{1}{11}$$\begin{vmatrix} 4 &1 \\\ -3& 2 \end{vmatrix}
so X=A-1B=\frac{1}{11}$$\begin{vmatrix} 4 &1 \\\ -3& 2 \end{vmatrix}$$\begin{vmatrix} -2 \\\ 3 \end{vmatrix}
$\Rightarrow \begin{vmatrix} x \\\ y \end{vmatrix}=\frac{1}{11}\begin{vmatrix} -8+3 \\\ 6+6 \end{vmatrix}=\frac{1}{11}\begin{vmatrix} -5 \\\ 12 \end{vmatrix}$=$\begin{vmatrix} -\frac{5}{11} \\\ \frac{12}{11} \end{vmatrix}$
Hence x=$-\frac{5}{11}$ and y=$\frac{12}{11}$