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.  
I know there is a way to go about this using matrices (we studied it 
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 
capabilities. The thing about this is to find the matrix equation you 
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/