Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

urgent! matrix help!

Announcements Posted on
Applying to Uni? Let Universities come to you. Click here to get your perfect place 20-10-2014
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    let A =

    i need to find a 5x5 matrix M with rank(M) = 2 that AM = 4X5 zero matrix.
    I thought of finding the inverse of A at first, but A is not a square matrix!!! i got stuck... help pls thanks!

    and for any 5X5 matrix B such that AB = 0 then rank B <= 2. how can i prove this?
    • 1 follower
    Offline

    ReputationRep:
    For the first bit, since rank(M) = 2 why don't you try:

    M = \begin{pmatrix} a & b & c & d & e \\f & g & h & i & j \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \end{pmatrix}?

    Then you could sub it in AM = 0 to find relations on a-j and just choose any old matrix that works.
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    omg are you saying i have to multiply that all out and solve for it? is there a proper way of doing it?
    • 0 followers
    Offline

    ReputationRep:
    That is the proper way of doing it. Pick any two linearly independent solutions of the system Ax=0. Then let B be the matrix whose first two columns are the solutions, and fill the remaining columns with zeros.

    You can do the second bit easily if you know the following inequality. If A is an mxn matrix, and B is an nxp matrix, then
    rank(A) + rank(B) - n <= rank(AB)

    (Try to justify it by drawing a diagram or something, if you don't feel like proving it carefully.)

    So in this case,
    3 + rank(B) - 5 <= 0
    => rank(B) <= 2

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: March 28, 2007
New on TSR

Personal statement help

Use our clever tool to create a PS you're proud of.

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.