In this exercise we prove that AP = P C for the matricesin Theorem 6.18. (This combined
Chapter 6, Problem 49(choose chapter or problem)
In this exercise we prove that AP = P C for the matricesin Theorem 6.18. (This combined with Exercise 50 proves thetheorem.)(a) Show that ARe(u)= Re(Au) and AIm(u)= Im(Au).(HINT: Recall that A is a real matrix.)(b) Use (a) and the identity u = Re(u) + iIm(u) to show thatARe(u)= aRe(u) + bIm(u),AIm(u)= bRe(u) + aIm(u)(HINT: Recall that u is an eigenvector of A with eigenvalue = a ib.)(c) Apply (b) to show that the columns of AP are the same as thecolumns of P C, and conclude AP = P C.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer