@Markiyan Hirnyk   for your interest! I meant that a segment is a closed interval. Of course easily to adjust procedure for all cases.

@Carl Love  I do not understand why on your images  additional lines appears, for example for k=1 .  Compare with my image:

F:=(x,y)->(1/2*x^2-3/2*y^3,-1/2*x^3+1/3*y^2):  # Nonlinear mapping R^2->R^2

X1:=t->(t,0): X2:=t->(0,t): X3:=t->(t,1): X4:=t->(1,t):

plot([[X1(t),t=0..1], [X2(t),t=0..1], [X3(t),t=0..1], [X4(t),t=0..1], [F(X1(t)), t=0..1], [F(X2(t)), t=0..1], [F(X3(t)), t=0..1], [F(X4(t)), t=0..1]], color=[red$4,blue$4], thickness=3, scaling=constrained);

@MDD  Your procedure was not working properly. What does  lt(p, T)  mean in it? An infinite loop occurs.

@shadi1386  Provide your data in Maple, rather than in Excel. I do not work with Excel.

@Markiyan Hirnyk  for useful information. I have Windows 8.1 64-bit

@rlopez  Should be  ctrl+l .

ctrl+L  does not work.

@farzane   

interface(rtablesize=infinity):

LinearAlgebra[RandomMatrix](8, 12);

convert({$1..12} minus {1,2,10,11}, list);

%%(..,%);

@Markiyan Hirnyk   I do not understand what you mean by this example? What sense to seek eigenvalues of a matrix consisting of polynomials?

mattcanderson1  If you are interested in a more detailed analysis of a curve of the second order, then you can download my procedure  QuadricCurveAnalysis  (in Russian)  here. In addition to making Maple for your example, it also finds: the eigenvectors and the eigenvalues of the corresponding quadratic form, the canonical equation of the parabola in the coordinates  x' , y', the parameter of the parabola  p , the equation of the axis of symmetry of the parabola, the connection between the original (in x , y  coordinates) and canonical coordinates, the angle of rotation of the canonical coordinate system relative to the original coordinate system and plots the parabola in original and canonical coordinates.

Here is the result of the work the procedure for your example: 

@Markiyan Hirnyk  I were writing my answer regardless of yours, and just before to post I saw your answer. I think for the questioner it's useful to read both answers because in some details, they are not identical.

@yunlongwang  You can not operate with  arbitrary matrices, only with matrices of predetermined sizes. You will not even can define an arbitrary matrix. See

A:=Matrix(n, symbol=a)  assuming n::posint;

  Error, (in Matrix) dimension parameters are required for this form of initializer

@Rouben Rostamian    Maybe   ode[i]$i=1..3;

@Carl Love  I remember that Maple does not recommend to solve the equations for expressions other than the names. Maybe I'm in something wrong.

solve(x^2+1=0, x^2);

@Markiyan Hirnyk  to restart and get result from the previous assumption.

@Markiyan Hirnyk  This is only a special case. The plane  l*x+m*y+n*z+p = 0  is defined, if  l^2+m^2+n^2<>0 . The condition  l<>0  is not equivalent to it.