# Thread: when solving a 2x3 equation applying the matrix system

1. ## when solving a 2x3 equation applying the matrix system

Hello.

When solving a 2x3 equation with the matrix system what is the goal? is it to end up with a zero like this?

a b c
0 d e

is that right? or should I also end up with a 1?

thank you.

2. Originally Posted by jhonwashington
Hello.

When solving a 2x3 equation with the matrix system what is the goal? is it to end up with a zero like this?

a b c
0 d e

is that right? or should I also end up with a 1?

thank you.
You need to be clearer about the exact nature of your question.

If your mean you have a set of equations:

$
a x + b y = c
d x + e y = d
$

which you are going to solve by reducing the augmented matrix:

$
\left[
\begin{array}
{cc|c} a&b&c\\d&e&f
\end{array}
\right]
$

by using row opperations.

How you do this depends on what you have been taught, but if you reduce
this to the form:

$
\left[
\begin{array}
{cc|c} g&0&h\\0&i&j
\end{array}
\right]
$

then $x=h,\ y=j$ is the solution to the original set of equations.

RonL