Associated Topics || Dr. Math Home || Search Dr. Math

### Matrices and TI Calculators

```
Date: 03/06/97 at 19:32:52
From: Erin Nichols
Subject: Solving polynomial equations using matrices on a TI-82

In studying equations for circles and parabolas of the general form
x^2 + Dx + Ey + F = 0, I encountered several problems that required
me to solve a system of three equations for the varaibles D, E, and F.
extensively in Algebra II) and a TI-82 calculator.

I remembered to enter the coefficients of the equations into a matrix,
and after that I was more or less stuck. Of course my book adequately
explains how to solve a problem like this with matrices (exchanging
rows of matrices and whatnot), but what I really want to know is how
to do it with my calculator since I'm not exactly interested in doing
the grunt work.

Thanks,
Erin
```

```
Date: 03/06/97 at 22:45:13
From: Doctor Charles
Subject: Re: Solving polynomial equations using matrices on a TI-82

Not many people enjoy doing 'grunt' work. I have a TI-85 but from my
understanding, it's pretty similar to a TI-82 in its matrix
are trying to solve. This means rearranging the equations so that they
all have the same form. Suppose that a,b,c,d,e,f,g,h,i,j,k,l are all
the numbers that are given in the problem. You want your equations to
look something like this:

aE + bF + cG = d
eE + fF + gG = h
iE + jF + kG = l

It is important to get all the E's first then the F's, etc. It should
just be a matter of putting everything onto the correct side of the
equation and getting the terms in the right order. Then you write the
three equations as one matrix equation:

_       _  _   _     _   _
|  a b c  ||  E  |   |  d  |
|  e f g  ||  F  | = |  h  |
|_ i j k _||_ G _|   |_ l _|

Now let A be the matrix on the left and we will call A- its inverse.
Then we can write:
_   _     _   _
|  E  |   |  d  |
A     |  F  | = |  h  |
|_ G _|   |_ l _|
_   _             _   _
|  E  |           |  d  |
|  F  | =   A-    |  h  |
|_ G _|           |_ l _|

So you would enter on your calculator something like this (replacing
a,b,c etc. for the actual numbers):

[[a,b,c][e,f,g][i,j,k]] -> A {enter}
| this arrow is the STO> key

Then: [d,h,l] -> B {enter}

To find the inverse of A, just type A then the x(-1) key ([2nd][EE])
A(-1)B {enter} should make the answer should appear:    [ D E F ]

-Doctor Charles,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculators, Computers
High School Linear Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search