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Math Help - Linear Algebra

  1. #1
    Junior Member
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    Linear Algebra

    a) Express the equations

    y1 = x1 - x2 + x3
    y2 = 3x1 + x2 - 4x3
    y3 = -2x1 - 2x2 + 3x3
    and
    z1 = 4y1 - y2 + y3
    z2 = -3y1 + 5y2 + 3x3

    in the matrix forms Y = AX and Z = BY. Then use these to obtain a direct relationship between Z and X.

    b) Use the equation Z = CX obtained in a) to express z1 and z2 in terms of x1, x2, and x3.

    c) Check the result in b) by directly substituting the equations for z1 and z2 and then simplifying.

    For Part A I have this so far:



    But I'm not sure how to switch the first matrices around so that I can have X = AY to match up with the Z = BY and find the relationship between them.

    In part b) I`m not really sure how the Z = CX works and how it can express z1 and z2 in terms of x1, x2, and x3.

    I think I could probably do part c if I figured out a and b though.

    Thanks a lot.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Adrian View Post
    a) Express the equations

    y1 = x1 - x2 + x3
    y2 = 3x1 + x2 - 4x3
    y3 = -2x1 - 2x2 + 3x3
    and
    z1 = 4y1 - y2 + y3
    z2 = -3y1 + 5y2 + 3x3

    in the matrix forms Y = AX and Z = BY. Then use these to obtain a direct relationship between Z and X.

    b) Use the equation Z = CX obtained in a) to express z1 and z2 in terms of x1, x2, and x3.

    c) Check the result in b) by directly substituting the equations for z1 and z2 and then simplifying.

    For Part A I have this so far:



    But I'm not sure how to switch the first matrices around so that I can have X = AY to match up with the Z = BY and find the relationship between them.

    In part b) I`m not really sure how the Z = CX works and how it can express z1 and z2 in terms of x1, x2, and x3.

    I think I could probably do part c if I figured out a and b though.

    Thanks a lot.
    well, if Y = AX and Z = BY, it means that Z = B(AX) doesn't it? thus we have that Z = CX, where C = BA
    Last edited by Jhevon; October 16th 2007 at 12:40 PM.
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  3. #3
    Junior Member
    Joined
    Sep 2007
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    I hadn't even thought of it that way, thanks a bunch.

    Wait, how do I multiply matrix A by matrix B, one is a 3x3 and the other is a 2x3.

    Nevermind, I just read, multiply in the order BA, not AB, which would then work, thanks again.
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