Results 1 to 4 of 4

Math Help - Matrices Problem?

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    7

    Matrices Problem?

    So I'm trying to solve this sample question because I'll be required to solve a similar one for an assignment but I'm not sure how to go about it.



    I know that A(^2) is (11, 28 ; 4, 11) and A(^4) is (233, 616 ; 88, 233)but I'm not sure how to find m and n, can anyone help? I don't even know if I can add a constant to a matrix.
    I'm more interested in how the question is done than the answer so a step by step would be appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,787
    Thanks
    1571

    Re: Matrices Problem?

    Quote Originally Posted by Daithi19 View Post
    So I'm trying to solve this sample question because I'll be required to solve a similar one for an assignment but I'm not sure how to go about it.



    I know that A(^2) is (11, 28 ; 4, 11) and A(^4) is (233, 616 ; 88, 233)but I'm not sure how to find m and n, can anyone help? I don't even know if I can add a constant to a matrix.
    I'm more interested in how the question is done than the answer so a step by step would be appreciated!
    So substitute these into your equation

    \displaystyle \begin{align*} \mathbf{A}^4 &= m\mathbf{A}^2 + n\mathbf{I}_2 \\ \left[\begin{matrix} 233 & 616 \\ 88 & 233  \end{matrix}\right] &= m\left[\begin{matrix} 11 & 28 \\ 4 & 11 \end{matrix}\right] + n\left[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}\right] \\ \left[\begin{matrix}  233 & 616 \\ 88 & 233 \end{matrix}\right] &= \left[\begin{matrix} 11m + n & 28m \\ 4m & 11m + n  \end{matrix}\right] \end{align*}

    So from here you can see

    \displaystyle \begin{align*} 233 &= 11m + n \\ 616 &= 28m \\ 88 &= 4m \end{align*}


    Solve this for \displaystyle \begin{align*} m \end{align*} and \displaystyle \begin{align*} n \end{align*}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    7

    Re: Matrices Problem?

    Ok so m = 22 and n = -9 , but do you mind explaining where you got the matrix that you multiplied by N from?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,787
    Thanks
    1571

    Re: Matrices Problem?

    Quote Originally Posted by Daithi19 View Post
    Ok so m = 22 and n = -9 , but do you mind explaining where you got the matrix that you multiplied by N from?
    You can't add scalars with matrices, so I multiplied the scalar by the identity matrix. This is a standard technique with matrix polynomials.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrices problem (gps)?
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: January 29th 2011, 04:10 AM
  2. Matrices problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 7th 2010, 05:01 AM
  3. Replies: 1
    Last Post: October 23rd 2010, 08:42 PM
  4. Matrices problem-
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 29th 2009, 07:35 AM
  5. matrices problem...
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 23rd 2009, 08:32 PM

Search Tags


/mathhelpforum @mathhelpforum