Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hence show that (Matrices)

  1. Aug 13, 2011 #1

    1.Show that B satisfies the equation (B-pI)(B-qI) = 0

    2.Hence, or otherwise, show that B-1 = 0.5(3I - B)

    In these kind of questions I don't know what they are testing me for! Let's take the first one as an example: The only skill they can possibly try to asses is whether I know how to multiply the matrix I by values I found previously (p and q). Other than that, all I can do to "answer" the question is performing the multiplication and showing it equals zero?

    For the second one it is even worst... I know how to calculate the inverse of B and when I do it does in fact equal 0.5(3I - B), but, what should I put on paper? Calculate the inverse the regular way and then perform 0.5(3I - B) and show the results are equal?

    I'm not sure if I was able to convey my doubt clearly... If the problem is due to lack of information in questions 1 and 2 I can add more information or rephrase my query.

    Peter G.
  2. jcsd
  3. Aug 13, 2011 #2


    User Avatar
    Homework Helper

    Is that all the question gives? Is B just a general nxn matrix or is it something given? (since you said you found values of p and q)

    You would just need to show that B, whatever that is will make that equation zero.

    For the second one, if you pre-multiply both sides B you might be able to factorize it in the form given in 1.
  4. Aug 13, 2011 #3
    Yeah, B is a 2x2 matrix. So I basically just multiply everything out and show it equals zero?

    For the second one you mean if I expand the first equation I can get the second one?

    Thanks once again,
    Peter G.
  5. Aug 13, 2011 #4


    Staff: Mentor

    Are you given a specific matrix B and values for p and q?
    Multiply 0.5(3I - B) by B for the matrix you are given (assuming you know B). If the expression simplifies to I, then 0.5(3I - B) is the inverse of B.
  6. Aug 13, 2011 #5

    Yeah, I have a specific value for both the matrix B, p and q.

    I got the second one now, thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook