You can use MATLAB to do matrix algebra for you,such as computing eigenvalues and eigenvectors.All of the matrices in this assignment have eigenvalues which are integers,and their eigenvectors can be written with integer components.

31 3) For the matrix C = ( 1 _.3 ) we stud).r the linear differential equation: % = C - Y. (a) laleulate the eigenvalues and corresponding cigeINcctors of the matrix C. This matrix C has two distinct, real eigenvalues. Write your eigenvectors V1 and V; so that each component of the vectors is an integer. (b) The linearity principal says that if Y1 and Y; are solutions then 31/363] = EH) + Yg) is also a solution. Find two straight line solutions 1/105) and Yg) such that EOE} := Y] (t) +Yg(t} is a solution with initial conditions Yam) = (4, 10]. (C) For this question you will produce three gures. Each gure should have a direction eld of the differential equation % = C -Y. On top of this direction eld plot the three solutions Fi), 1/265), Kit] from part [b] for time 0 S t