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Math Help - [SOLVED] Solving if a matrix is infinite

  1. #1
    Junior Member Evales's Avatar
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    [SOLVED] Solving if a matrix is infinite

    x + y + z = 4
    2x + 3y + z = 8
    3x + (3-p)y + 2z = 13-(p^2)

    I've reduced the system of equations to:

    x + y + z = 4
    y - z = 0
    (p+1)y = (p^2) - 1

    It then says:

    "For each of p = 1 and p = -1 indicate how many solutions there are to the system of equations. I there is a unique solution, give that solution. If there are infinitely many solutions give the resulting unique solution when
    (i) z = 1
    (ii) z = -1

    I've found that p=1 give unique and p = -1 give infinite.

    PS. My elimination is fine I have the answers.
    (i) z = 1, y = 1, x = 6
    (ii) z = -1, y = -1, x = 6

    I just don't know how to solve if it is infinite.
    Last edited by Evales; June 6th 2008 at 09:45 PM. Reason: Missing information
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Evales View Post
    x + y + z = 4
    2x + 3y + z = 8
    3x + (3-p)y + 2z = 13-(p^2)

    I've reduced the system of equations to:

    x + y + z = 4
    y - z = 0
    (p+1)y = (p^2) - 1

    It then says:

    "For each of p = 1 and p = -1 indicate how many solutions there are to the system of equations. I there is a unique solution, give that solution. If there are infinitely many solutions give the resulting unique solution when
    (i) z = 1
    (ii) z = -1

    I've found that p=1 give unique and p = -1 give infinite.

    PS. My elimination is fine I have the answers.
    (i) z = 1, y = 1, x = 6
    (ii) z = -1, y = -1, x = 6

    I just don't know how to solve if it is infinite.
    If p=-1

    The last equation turns into 0=0 That is true for all values of y.

    so let y=t

    subbing into the equation above it you get
    t-z=0 \iff z=t

    subbing both of these back into the first equation we get

    x+t+t=4 \iff x=-2t+4 then the general solution is

    (-2t+4,t,t) \\\ t \in \mathbb{R}

    I hope this helps.
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  3. #3
    Junior Member Evales's Avatar
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    Yup tis all good thanks!
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