In: Advanced Math
Let A be a square matrix defined by
(a) Find the eigenvalues and eigenspaces of A.
(b) Show that A is diagonalizable. Diagonalize A.
Solution
a. Find the eigenvalue and eigenspaces of. A.
Find The eigenspaces associated to eigenvalues
Therefore, the eigenspace associated to
(b) Show that $A$ is diagonalizable. Diagonalize A.
(c) Solve the system of linear differential equations dx/dt=Ax
The general solution to the system is:
Therefore, the solution of system becomes: