Results 1 to 4 of 4

Math Help - Practical Applications of Matrices

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    94

    Practical Applications of Matrices

    I'm looking to understand practical applications of matrices, involving flow of water. One such question is this:

    The attached figure shows known flow rates of hydro carbons into and out of a network of pipes at an oil refinery.
    a) Set up a linear system whose solution provides the unknown flow rates.
    b) Solve the system for the unknown flow rates.
    c) Find the flow rates and directions of flow if x4=50 and X6=0.

    I have attached a crudely drawn representation of the figure I am supposed to use. I know how to figure out missing values for a two dimensional figure, but I'm unsure of how to do a three dimensional one...
    Attached Thumbnails Attached Thumbnails Practical Applications of Matrices-mathproblem.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by Hellreaver View Post
    I'm looking to understand practical applications of matrices, involving flow of water. One such question is this:

    The attached figure shows known flow rates of hydro carbons into and out of a network of pipes at an oil refinery.
    a) Set up a linear system whose solution provides the unknown flow rates.
    b) Solve the system for the unknown flow rates.
    c) Find the flow rates and directions of flow if x4=50 and X6=0.

    I have attached a crudely drawn representation of the figure I am supposed to use. I know how to figure out missing values for a two dimensional figure, but I'm unsure of how to do a three dimensional one...
    the linear system you're looking for is this:

    x_1-x_2=-25

    x_1+x_3=200

     x_3-x_4-x_5=-150

    x_2+x_4-x_6=175

    x_5+x_6=200.

    now solve the equation by reducing the following matrix to echelon form:

    \begin{bmatrix}1 & -1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & -1 & 0 \\ 0 & 1 & 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 1 & 1 \end{bmatrix}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    94
    Why is the last column of the matrix 0s and 1s? Shouldn't it be the constants in the linear system?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by Hellreaver View Post
    Why is the last column of the matrix 0s and 1s? Shouldn't it be the constants in the linear system?
    sure, i forgot! so \begin{bmatrix}-25 \\ 200 \\ -150 \\ 175 \\ 200 \end{bmatrix} is the seventh column of the matrix.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Special Matrices and Applications
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 18th 2011, 12:14 PM
  2. Singular Value Decomposition practical applications
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 8th 2009, 10:29 AM
  3. Applications of matrices II
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 18th 2008, 11:12 AM
  4. Applications of matrices
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 18th 2008, 10:15 AM
  5. Practical use of Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 23rd 2006, 11:22 PM

Search Tags


/mathhelpforum @mathhelpforum