Question

In: Advanced Math

Systems of Ordinary Differential Equations

Let A be a square matrix defined by

(a) Find the eigenvalues and eigenspaces of A.

(b) Show that A is diagonalizable. Diagonalize A.

Expert Solution

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:

SUN BUNRA answered 3 years ago

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