Matrices and TI CalculatorsDate: 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/ |
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