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Homework Help: 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:




    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


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    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


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    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).
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