1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Algebra Systems of Equations

  1. Sep 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the following two system of equations:

    y[itex]_{1}[/itex]=-2x[itex]_{1}[/itex]-x[itex]_{2}[/itex]+2x[itex]_{3}[/itex]
    y[itex]_{2}[/itex]=2x[itex]_{1}[/itex]+2x[itex]_{2}[/itex]-3x[itex]_{3}[/itex]
    y[itex]_{3}[/itex]=-2x[itex]_{1}[/itex]-2x[itex]_{2}[/itex]+2x[itex]_{3}[/itex]

    and

    z[itex]_{1}[/itex]=3y[itex]_{1}[/itex]-4y[itex]_{2}[/itex]-3y[itex]_{3}[/itex]
    z[itex]_{1}[/itex]=3y[itex]_{1}[/itex]-y[itex]_{2}[/itex]-4y[itex]_{3}[/itex]

    Rewrite these 2 systems as Ax=y and By=z. Use this to get C so that Cx=z.
    a) What is the matrix C?

    B) Find the RREF matrix D which is row equivalent to the augmented matrix [C|z]

    3. The attempt at a solution
    My initial thought was that the matrix A would be:
    -2 -1 2
    2 2 -3
    -2 -2 2

    and matrix B:
    3 -4 -3
    3 -1 -4
    and that C would be the product of A and B. However, I realized that since the column of A isn't the same as the row of B I couldn't form a product with them. I'm lost on how to find the matrix C. Do I need to invert a matrix in order to find C (the product)?
     
  2. jcsd
  3. Sep 6, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, you don't. Your have Ax= y and By= z. Replace y in the second equation by Ax.
     
  4. Sep 6, 2011 #3
    I'm sorry I don't understand what you mean. Are you saying the matrix A is right but I would have to substitute matrix B with Ax instead of y? I don't get how I would replace y with Ax. My thought is that i would multiply the coefficients of y in the matrix b with the coefficients of x in matrix a.
     
  5. Sep 7, 2011 #4

    BruceW

    User Avatar
    Homework Helper

    Well, you had y=Ax and z=By, so replacing y with Ax gives: z=BAx. I think you came across problems because you tried to calculate AB (which is the wrong order).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear Algebra Systems of Equations
Loading...