Similar to problem 8 of homework 9, use the method of eigenvalue and eigenvector to solve the following system of differential equations. dx1 dt = −x1 + 4x2 + 2x3 dx2 dt = 4x1 − 1x2 − 2x3 dx3 dt = 0x1 + 0x2 + 6x3

that is, write the above system in matrix form x0 = ax, then find a matrix p such that p −1ap = d, where d is some appropriate diagonal matrix.

after that, use the substitution x = p y to decouple the system into differential equations in y, solve that system, and convert it back to x.