Question

How do you use matrices to solve systems of polynomial equations?

Answer 1

See general description below:

Explanation:

Uses Gaussian elimination. Basically it is the same process you adopt when you first came across Simultaneous equations. It just has a slight twist to it. You change one row (equation) so that you can them eliminate by subtraction or addition. It usually takes several stages to obtain a complete answer.

Suppose we had:

`3x+ 2y =6`
`-5x +10y =23`

These numbers are off the top of my head so I have no idea how they would turn out!

You would then write them out in Matrix form

x y answer
3 2 6
-5 10 23

You would manipulate these until you get:

x y answer
1 0 some value
0 1 some other value

So for the first row you have 1 of x but none of y. So the value in 'answer' is the value of x

The second row is the same for y
It is not really necessary all of the time to have all the ones sloping down from top left to bottom right.. If you do this is called 'Row Echelon' form. However it is more tidy to do so and situations do exist where it is important they are in this form

If you type Echelon form into google and look at images you will see examples.