Suppose P is invertible and A=PBP^(-1). Solve for B in terms of A.?

NetherCraft 0

2 Answers

  • Multiply both sides on the left by P^(-1):

    P^(-1)A = P^(-1)(PBP^(-1))

    ==> P^(-1)A = (P^(-1) P)BP^(-1)

    ==> P^(-1)A = I BP^(-1)

    ==> P^(-1)A = BP^(-1).

    Next, multiply both sides on the right by P:

    (P^(-1)A) P = (BP^(-1)) P

    ==> P^(-1)AP = B (P^(-1) P)

    ==> P^(-1)AP = BI

    ==> P^(-1)AP = B.

    I hope this helps!

  • For the best answers, search on this site

    First right multiply by P: AP = PBP^(-1)P = PB Now left multiply by P^(-1): P^(-1)AP = P^(-1)PB = B.

Also Check This  Would a horse enjoy a bounce house?

Leave a Reply

Your email address will not be published. Required fields are marked *