Characteristic Polynomial And Eigenvalues - Texas Instruments TI-86 Manual Book

252
Chapter 19: Applications
The first eigenvalue is real,
since the imaginary part is .
0
If necessary, select
ALL-
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
On the home screen, select
menu, and then press b to run the program.
When prompted, enter:

Characteristic Polynomial and Eigenvalues

In the matrix editor or on the home screen, enter matrix
[[L1,2,5][3,L6,9][2,L5,7]]¶A
On the home screen, select
to find the complex eigenvalues for the matrix
to the list name EV .
Graph the characteristic polynomial Cp(x) of matrix
Cp(x) based on the formula Cp(x)=det(A
menu and enter the function in the equation editor as shown.
GRAPH
»y1=det (ANx¹ident 3)
Select WIND from the
xMin=L10 xMax=10
Select ROOT from the
the real eigenvalue interactively. Use
Right Bound=L4 , and
Compare the root ( x value) you displayed interactively with the
first element of the result list in step 2.
TAYLOR from the PRGM NAMES
FUNCTION: sin x
ORDER: 5
CENTER: 0
eigVl from the
MATRX MATH
A
N x¹I). In
GRAPH menu and set the window variable values as shown.
xScl=1 yMin=L100
GRAPH MATH menu and use it to display
Left Bound=L5
Guess=L4.5 .
as shown.
A
menu
and store them
A without knowing the analytic form of
Func graphing mode, select
yMax=50 yScl=10
,
y(x)= from the
xRes=4