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Math Help - Need help solving equations from this matrix

  1. #1
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    Need help solving equations from this matrix

    I have a matrix

    1 0 5 0 0
    0 1 1 5 0
    0 0 0 0 1

    Which gives the three equations:

    X1 + 5X3 = 0
    X2 + X3 + 5X4 = 0
    4X5 = 0

    Now in my notes it says that you can solve it to get:

    X1 = 2X3 + 0X4
    X2 = 6X3 + 2X4
    X3 = 1X3 + 0X4
    X4 = 0X3 + 1X4
    X5 = 0X3 + 0X4

    Could someone help explain to me how you go from the first equations to the second, for the life of me i can't figure it out
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  2. #2
    Junior Member
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    Oct 2009
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    I've been looking at this for a while myself..!

    I am no genius, but are you sure you are looking on the right notes?

    How can x_1 + 5x_3 = 0 go to x_1 = 2x_3, unless x_3 = 0 I guess?
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  3. #3
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    Joined
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    Yeah i just double checked the notes, that's exactly what it says. And there not my notes either there the lecturers.

    Can't understand what's happening and he dosen't explain it anywhere, it's to do with finding the complete solution to this system of linear equations.
    Where these two are matricies.

    4 2 1 3 6 ......4
    0 3 3 1 0.x.=..6
    3 2 4 1 5 ......2

    over Z7

    Firstly he applies GJ to the whole lot in one matrix to get:

    1 0 5 0 0 3
    0 1 1 5 0 2
    0 0 0 0 1 2

    Then he splits the matrix into to and gets:

    ......3
    ......2
    G....0
    ......0
    ......2

    1 0 5 0 0
    0 1 1 5 0....=....0
    0 0 0 0 1

    Then he solves to get the equations listed above
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  4. #4
    MHF Contributor

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    Quote Originally Posted by BigBoss22 View Post
    I have a matrix

    1 0 5 0 0
    0 1 1 5 0
    0 0 0 0 1

    Which gives the three equations:

    X1 + 5X3 = 0
    X2 + X3 + 5X4 = 0
    4X5 = 0

    Now in my notes it says that you can solve it to get:

    X1 = 2X3 + 0X4
    From the first equation above, X1= -5X3, not 2X3

    X2 = 6X3 + 2X4
    and X2= -X3- 5X4, not 6X3+ 2X4

    X3 = 1X3 + 0X4
    X4 = 0X3 + 1X4
    X5 = 0X3 + 0X4
    The last equation in the set clearly says that X5= 0.

    Could someone help explain to me how you go from the first equations to the second, for the life of me i can't figure it out
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