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Math Help - Linear Equations: Determine the values of a in this system of linear equations

  1. #1
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    Linear Equations: Determine the values of a in this system of linear equations

    Hi,

    I have a question regarding linear algebra which I am unsure of how to approach. The question says:

    Determine the values of a for which the following system of equations has (a) no solutions, (b) exactly one solution, and (c) infinitely many solutions.

    x + y + 7z = -7
    2x + 3y + 17z = -16
    x + 2y + (a^2+1)z = 3a

    So I assume that we would use some form of Gaussian to figure out the solutions because thats what have have been doing in the course so far, but everything I have tried so far has failed!!!

    I did get a solution of a=3 for no solutions, but I'm not actually sure if this is correct (what I did was set a^2-6 equal to 3 after using row reduction). Anyway any help I could get would be greatly appreciated or even just any clues as to how I should start this problem.

    Thanks in advance!!
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  2. #2
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    Re: Linear Equations: Determine the values of a in this system of linear equations

    Gaussian elimination is the right way to go.
    Having done that the third equation is
    (a^{2}-9)z=3a+9.
    You have to figure out what this implies for various values of a.
    Specifically those that make the z coefficient zero.
    Thanks from Cotty
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  3. #3
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    Re: Linear Equations: Determine the values of a in this system of linear equations

    Ohhh thank you very much, i think i might be on the right track now
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  4. #4
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    Re: Linear Equations: Determine the values of a in this system of linear equations

    So the solutions I found are:

    For no solution: a=3
    For infinitely many solutions: a=-3
    and
    For one solution: a E {R/(-3,3)}

    Sorry with that last one I know how I've written it probably isn't the correct way to write it mathematically but what i meant is that a is an element of the Real number system not including -3 and 3 (if you could show me how to write this properly it would be very appreciated as it has been a while since I have done that type of stuff). Are these the correct solutions?

    Anyway thank-you very much for the help you have given me so far!
    Last edited by Cotty; March 6th 2013 at 05:45 AM.
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