Question

Examine the consistency of the system of equations.
x+2y=2,
2x+3y=3

Answer 1

The given system of equations is:
x + 2y = 2
2x + 3y = 3
The given system of equations can be written in the form of AX = B, where

A= $\begin{bmatrix}1&2\\\2&3\end{bmatrix}$,X=$\begin{bmatrix}x\\\y\end{bmatrix}$ and B=$\begin{bmatrix}2\\\3\end{bmatrix}$
Now,
IAI=1(3)-2(2)=3-4=-1≠0
∴ A is non-singular.
Therefore, A-1 exists.

Hence, the given system of equations is consistent.