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=$\begin{bmatrix}2&-1\\\3&4\end{bmatrix}$,X =$\begin{bmatrix}x\\\y\end{bmatrix}$and B=$\begin{bmatrix}-2\\\3\end{bmatrix}$
Now, |A|=8+3=11≠0
Thus, A is non-singular.
Therefore, its inverse exists.

Now, A-1=$\frac{1}{\mid A\mid}$adj A=\frac{1}{11}$$\begin{bmatrix}4&1\\\\-3&2\end{bmatrix}

∴X=A-1 B=\frac{1}{11}$$\begin{bmatrix}4&1\\\\-3&2\end{bmatrix}$$\begin{bmatrix}-2\\\3\end{bmatrix}

$\Rightarrow\begin{bmatrix}x\\\y\end{bmatrix}$= \frac{1}{11}$$\Rightarrow\begin{bmatrix}-8+3\\\6+6\end{bmatrix}

=\frac{1}{11}$$\Rightarrow\begin{bmatrix}-5\\\12\end{bmatrix}=$\begin{bmatrix}\frac{-5}{11}\\\\\frac{12}{11}\end{bmatrix}$

Hence, x=$-\frac{5}{11}$ and y=$\frac{12}{11}$