Change of basis and model matrix

Hi,

I am not able to understand the question properly,please can you explain with solution.This is the question,

Consider a system of differential equations of the kind

dx

(t)/dt= Ax(t)

where

x is a state (column) vector and A is a matrix. With a transformation of the state vector as x = M^x

the system can be written as

d

^x

dt

=

A^x^(t)

where

A^ = M-1AM. Choose M as the ”model matrix”, i.e. M = [e1; e2; e3], where ei, i = 1; 2; 3 are the

eigenvectors of A, and calculate A^ for the following problems

**Please note: It is A^ -A cap and M^ -M cap**

** M-1 is M inverse**