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Homework Help: Matrix ?

  1. Mar 30, 2008 #1
    solve eqautions using a matrix

    x + y -z = 0
    3x - y + z = 4
    5x +z = 7

    so i wrote the matrix

    1 1 -1 0
    3 -1 1 4
    5 0 1 7

    then i multiplied Row 1 by -3 and added that to row 2
    and multiplied row 1 by -5 and added that to row 3
    resulting in

    1 1 -1 0
    0 -4 4 4
    0 -5 6 7

    then i multiplied row 2 by - 1/4

    1 1 -1 0
    0 1 -1 -1
    0 -5 6 7

    then multiplied row 2 by 5 and added that to row 3

    1 1 -1 0
    0 1 -1 -1
    0 0 1 2

    now i subbed back in to eqns

    x + y -z = 0
    3x - y + z = 4
    5x +z = 7

    1x + 1y - 1z = 0
    0x +1y - 1z = -1
    0x + 0y + 1z = 2

    so z = 2 and solving all the other equation i get x = 1 and y = 1
    is this right because i tried solving these by subtraction and got somthing different
     
    Last edited: Mar 30, 2008
  2. jcsd
  3. Mar 30, 2008 #2

    neu

    User Avatar

    You have not constructed a matrix equation, you have just rewritten the coefficients in some kind of array/pattern

    THe matrix equation is :

    [tex]\begin{pmatrix}
    1 & 1 & -1\\
    3&-1 & 1\\
    5&0&1
    \end{pmatrix}
    \begin{pmatrix}
    x\\
    y\\
    z
    \end{pmatrix}
    =
    \begin{pmatrix}
    0\\
    4\\
    7
    \end{pmatrix}

    [/tex]
     
    Last edited: Mar 30, 2008
  4. Mar 30, 2008 #3
    The augmented matrix that 2slow to go fast used is correct.
    All you need to do is plug x y and z back into your original equations and see if they make true statements.
    Looks to me like they check out.
    CC
     
  5. Mar 30, 2008 #4
  6. Mar 30, 2008 #5
    i just got it i was substituting wrong thanks for the help
     
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