Results 1 to 3 of 3

Math Help - Solving matrix equations

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    1

    Solving matrix equations

    Is there any way to solve matrix equations A=BX, where A, B and X are all n*n matrices, and you know A and B but not X, and det(A)=det(B)=0, so you can't use an inverse?

    If there's no generalized way, is there any theory about how to get started on this problem? Any links or references would be appreciated.

    Google can't seem to focus on this particular topic because anytime you search for solving matrix equations, you get links to solving Ax=b, where x and b are vectors and not matrices.

    Thanks much!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by phileas View Post
    Is there any way to solve matrix equations A=BX, where A, B and X are all n*n matrices, and you know A and B but not X, and det(A)=det(B)=0, so you can't use an inverse?

    If there's no generalized way, is there any theory about how to get started on this problem? Any links or references would be appreciated.

    Google can't seem to focus on this particular topic because anytime you search for solving matrix equations, you get links to solving Ax=b, where x and b are vectors and not matrices.

    Thanks much!

    Try looking for decompostion of matrices.
    LU decomposition.
    Upper & Lower trianglular matrix manipulation.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    From what I understand, you are looking to solve a matrix equation like this,

    \begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\\ \end{bmatrix}<br />
x=\begin{bmatrix}b_{11} & b_{12} \\b_{21} & b_{22} \\ \end{bmatrix}

    yes/no?

    We can creat two equations from this...

    Equation 1
    \begin{bmatrix}a_{11}\\a_{21}\\ \end{bmatrix}x_{1}+\begin{bmatrix}a_{12}\\a_{22}\\ \end{bmatrix}x_{2}=\begin{bmatrix}b_{11}\\b_{21}\\ \end{bmatrix}

    and...

    Equation 2
    \begin{bmatrix}a_{11}\\a_{21}\\ \end{bmatrix}x_{1}+\begin{bmatrix}a_{12}\\a_{22}\\ \end{bmatrix}x_{2}=\begin{bmatrix}b_{12}\\b_{22}\\ \end{bmatrix}

    Solving for equation 1 we get...

    \begin{bmatrix}x_{11} & ...\\x_{21} & ...\\ \end{bmatrix}

    Solving for equation 2 we get...

    \begin{bmatrix}x_{11} & x_{12}\\x_{21} & x_{22}\\ \end{bmatrix}

    Which is the answer. Sorry, If I have over simplified your problem. This is just what I got form it.
    Last edited by Danneedshelp; June 20th 2009 at 05:23 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving matrix equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 10th 2010, 10:39 AM
  2. Matrix equations solving help needed?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: January 20th 2010, 06:12 AM
  3. Solving equations - Matrix Help!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 10th 2010, 10:32 AM
  4. Need help solving equations from this matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 3rd 2009, 04:46 AM
  5. Matrix Inverse solving system of equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 15th 2009, 04:48 AM

Search Tags


/mathhelpforum @mathhelpforum