Dear Hamed...If I understood correctly, you calculated both the eigen values and the two eigen vectors for the problem. Please be much more clear about your question. And also if you see, about 96.3 % is from second eigen value in your calculation (1.28...). So, one eigen vector is sufficient to proceed further analysis. To present the data in the principal component space, you have to calculate and scores and loadings of the data matrix. You can sue "Multivariate analysis" - Adds In in excel to do this or other wise MATLAB.

Thanks sir Sree for your answer but i was wondering how can i compute the X and Y value from the two equations?

i finally reached that choosing the X and Y values are random?? is this true.

If you are looking for the X and Y values please refer to three possible solutions of your linear problem. Finite and unique solutions, Infinitely many solutions and No solution. you can refer to any basic Linear algebra book for further details.

The above system of equations has a singular matrix. I propose to solve one of the following two systems of equations:

First system:

0.567472154X + 0.615444444Y = 0

X + Y = 1

Second system:

0.615444444X + 0.667472154Y = 0

X + Y = 1

This will allow to find eigenvector with unit length.

That's enough for a 2-D case. For more dimensions, I suggest numerical methods. Probably the easiest to implement is Jacoby's method.

A bit more about PCA: https://www.researchgate.net/publication/319469038_New_Interpretation_of_Principal_Components_Analysis

Article New Interpretation of Principal Components Analysis