**Toolbox:**

- (i)A matrix is said to be invertible if inverse exists.
- (ii)If A is a non singular matrix such that
- AX=B
- then X=$A^{-1}B$
- using this we can solve system of equations,which has unique solutions.

The given system of equation is

x+2y=2

2x+3y=3

This can be written in the form AX=B,

$A=\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\;X=\begin{bmatrix}x\\y\end{bmatrix}\;B=\begin{bmatrix}2\\3\end{bmatrix}$

Hence $\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\3\end{bmatrix}$

Now let us find the value of the determinant

|A|=3-2=1$\neq 0$

Hence A is non-singular.

Therefore $A^{-1}$ exists.

Hence the given system is consistent.

edited Feb 27, 2013 by trsarathi