Chapter 5

Question 1

A Procedure for Solving y’ = Ay if A is Diagonalizable

Answer 1

Step 1: Find a matrix P that diagonalizes A.

Step 2: Make the substitutions: y = Pu and y’ = Pu’ to obtain a new “diagonal system” u’ = Du, where D = P^-1AP

Step 3: Solve u’ = Du

Step 4: Determine y from the equation y = Pu