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Algebra question again

  1. Oct 23, 2005 #1
    Hey again!
    Im having trouble with this problem given in the matrix inverse section of the textbook. It gives these two matricies in the form AX=B
    [x1]=[3 -1 2][y1]
    [x2]=[1 0 4][y2]
    [x3]=[2 1 0][y3]
    and
    [z1]=[1 -1 1][y1]
    [z2]=[2 -3 0][y2]
    [z3]=[-1 1 -2][y3]
    The question says, given the first matrix and the second matrix, express the variables, x1, x2, x3 in terms of z1, z2, z3. Im not too sure on where to start here. So far, I just multiplied through to find the equations for the x variables and z variables.
    x1 = 3y1 - y2 + 2y3
    x2 = y1 + 4y3
    x2 = 2y1 + y2
    z1 = y1 - y2 + y3
    z2 = 2y1 - 3y2
    z3 = -y1 + y2 + 2y3
    Im not sure on where to go from here.
    Thanks in advance
     
  2. jcsd
  3. Oct 23, 2005 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If Y= AX and Z= BY then Z=B(AX)= (BA)X and so X= (BA)-1Z= (A-1B-1)Z. Can you find the inverses of those matrices?
    (Or multiply them and then find the inverse of the product.)
     
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