Results 1 to 3 of 3

Math Help - Matrix system

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    5

    Exclamation Matrix system

    Hey all. a 3 sector model problem, lets jus say not may expertise any help would be great!
    Thanks and God bless Bob
    Attached Thumbnails Attached Thumbnails Matrix system-probllemas.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,897
    Thanks
    327
    Awards
    1
    Quote Originally Posted by bobby87 View Post
    Hey all. a 3 sector model problem, lets jus say not may expertise any help would be great!
    Thanks and God bless Bob
    You have the equations:
    Y = C + I^* + G^*
    C = a(Y - T) + b
    T = tY + T^*

    You want this in the form
    Ax = B <-- I'm using a B to distinguish this from b.

    So in the equations put all the Y, C, and T terms on the LHS and everything else on the right:
    Y - C = I^* + G^*
    C - aY + aT = b
    T - tY = T^*

    Now arrange the variables Y, C, T in that order in the equations. If a term doesn't exist, give it a 0 coefficient:
    1 \cdot Y - 1 \cdot C + 0 \cdot T = I^* + G^*
    -aY + 1 \cdot C + aT = b
    -tY + 0 \cdot C + 1 \cdot T = T^*

    Now you should be able to verify that
    \left ( \begin{matrix} 1 & -1 & 0 \\ -a & 1 & a \\ -t & 0 & 1 \end{matrix} \right ) \cdot \left ( \begin{matrix} Y \\ C \\ T \end{matrix} \right ) = \left ( \begin{matrix} I^* + G^* \\ b \\ T^* \end{matrix} \right )

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,897
    Thanks
    327
    Awards
    1
    You have the matrix equation:
    \left ( \begin{matrix} 1 & -1 & 0 \\ -a & 1 & a \\ -t & 0 & 1 \end{matrix} \right ) \cdot \left ( \begin{matrix} Y \\ C \\ T \end{matrix} \right ) = \left ( \begin{matrix} I^* + G^* \\ b \\ T^* \end{matrix} \right )

    Cramer's rule says that
    Y = \frac{ \left | \begin{matrix} I^* + G^* & -1 & 0 \\ b & 1 & a \\ T^* & 0 & 1 \end{matrix} \right | }{ \left | \begin{matrix} 1 & -1 & 0 \\ -a & 1 & a \\ -t & 0 & 1 \end{matrix} \right | }

    I'll let you work the determinants. For verification I get that:
    Y = \frac{b + I^* + G^* - aT^*}{a(t - 1) + 1}

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Coordination System Change Matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 18th 2011, 12:35 AM
  2. Setting up a system of equations for a matrix
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 29th 2010, 03:06 AM
  3. matrix system of equations help
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 31st 2009, 12:09 PM
  4. Matrix System for Solving
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 29th 2008, 06:10 PM
  5. Explanation of a matrix, linear system
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: June 11th 2008, 08:00 PM

Search Tags


/mathhelpforum @mathhelpforum