On of the most useful brand of mathematics is linear algebra , which have more application in science and engineering , because it required the description of some measurable quantities. In  this research paper determine some application of Eigen value problems. Obtain the principal direction of the position vector x of P(x,y) for which the f the position vector y of q have the similar or exactly opposite direction, find the shape of the circle after the instability.  How to obtain the Eigen value and Eigen vector of square matric and characteristic equation and polynomial . Apply the solution of Eigen value problem to stretching of elastic membrane, arising from population model and vibrating  system of two masses on two springs problems . The Leslie model describes age- specified population  growth, Mas-spring system involving several masses and spring can be trated as eigenvalue problems. This procedure also used for calculating some other physical and biological problem like arising of Markov processes problem.