Results 1 to 2 of 2

Math Help - Proofs in linear algebra

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    7

    Proofs in linear algebra

    I'm in a linear algebra class and I'm quite new to proofs... In my textbook there are quite a bit of questions that says to prove a bunch of properties and whatnot.

    For example...

    How would I go about proving

    (A^T)^p = (A^p)^T

    where p is a non-negative integer and A is a square matrix. (T = transposed)

    Or

    If A and B is a n x n matrix, prove that AB = BA


    How do I prove these? Do I provide an example or something or do I have to do something with summation notation?

    A hint/guide would be very helpful. Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    1) Use the equality: (A\cdot B)^T=B^T\cdot A^T

    If B=A then (A^2)^T=(A^T)^2

    In a similar way you can prove the general case.

    2) The equality AB=BA is not true for all A and B.

    For example, if A=\begin{pmatrix}1 & 0\\2 & 0\end{pmatrix}, \ B=\begin{pmatrix}1 & -1\\0 & 0\end{pmatrix} then

    AB=\begin{pmatrix}1 & -1\\2 & -2\end{pmatrix}, \ BA=\begin{pmatrix}-1 & 0\\0 & 0\end{pmatrix}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linear algebra - concept proofs
    Posted in the Advanced Algebra Forum
    Replies: 34
    Last Post: August 2nd 2010, 04:32 AM
  2. Linear algebra proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 5th 2010, 12:19 PM
  3. linear algebra proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 2nd 2010, 09:25 PM
  4. linear algebra proofs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 20th 2010, 11:06 PM
  5. 3 Advanced Linear Algebra Proofs
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 29th 2009, 06:12 AM

Search Tags


/mathhelpforum @mathhelpforum