Results 1 to 5 of 5

Math Help - Finding two matrices that multiply to...

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    Finding two matrices that multiply to...

    First of all, what is meant by a numerical matrix?
    Is it a matrix whose ij entries are not 0?
    Is it a matrix whose ij entries have at least 1 number?

    What are 2 numerical, 3x3, matrices A, B that multiply to the 0 matrix and A and B are not zero matrices themselves.

    I have a simple solution to this depending on the definition of a numerical matrix. If it is the first definition then I need an example.

    Also, how do I find a 3x3 matrix B such that for every 3x3 matrix A, AB = 3B?
    I don't think it's possible, what if A is a zero matrix?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by Noxide View Post

    What are 2 numerical, 3x3, matrices A, B that multiply to the 0 matrix and A and B are not zero matrices themselves.
    If A \times B = 0 then A or B must also be zero.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    158
    Quote Originally Posted by pickslides View Post
    If A \times B = 0 then A or B must also be zero.

    I don't think this is true at all... maybe for invertible matrices?
    For example, let x1 = x2 = x3 = (1, -2, 1) = rows of the matrix A
    and let y2 = y3 = y4 = (2, 2, 2) = columns of the matrix B
    AB = 0...

    What if we just let 1 of the matrices be invertible?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328
    Quote Originally Posted by Noxide View Post
    First of all, what is meant by a numerical matrix?
    Is it a matrix whose ij entries are not 0?
    Is it a matrix whose ij entries have at least 1 number?
    A numerical matrix is simply a matrix whose entries are numbers. There is no requirement that the any of the entries be non-zero.

    What are 2 numerical, 3x3, matrices A, B that multiply to the 0 matrix and A and B are not zero matrices themselves.

    I have a simple solution to this depending on the definition of a numerical matrix. If it is the first definition then I need an example.
    How about A= \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix} and B= \begin{bmatrix}1 & 1 \\ -1 & -1\end{bmatrix}

    Also, how do I find a 3x3 matrix B such that for every 3x3 matrix A, AB = 3B?
    I don't think it's possible, what if A is a zero matrix?
    Yes, you are right.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328
    Quote Originally Posted by pickslides View Post
    If A \times B = 0 then A or B must also be zero.
    Sorry, but that is completely false! We are talking about matrices here, not numbers. The ring of matrices has "zero divisors".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding Elementary Matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 7th 2011, 02:01 AM
  2. Help finding determinants of matrices
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: July 4th 2010, 05:17 PM
  3. Finding examples of 3X3 matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 10th 2010, 02:31 PM
  4. Finding all 2 by 2 matrices that have eigenvalues x and y
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 5th 2009, 04:46 PM
  5. Multiply 2 Matrices to find ABCD in Matrix B
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 1st 2009, 08:09 PM

Search Tags


/mathhelpforum @mathhelpforum