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    When writing my maths notes and doing the questions, I'm stumped on the following simulatenous equations:

     a + b + c = 0

    2a + c = 0

    I know that c = -2a and a = b , but I'm not sure how to find the values. Any help would be appreciated
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    (Original post by SecretDuck)
    When writing my maths notes and doing the questions, I'm stumped on the following simulatenous equations:

     a + b + c = 0

    2a + c = 0

    I know that c = -2a and a = b , but I'm not sure how to find the values. Any help would be appreciated
    What you have is a system of two equations in three variables. That means it's underdetermined: the solutions, if they exist, are not unique. You've reduced them to their simplest form, such that given a, you can produce a solution (a,b,c) = (a,a,-2a); that's the best you can do.

    That is to say, the solution to the system is precisely b=a, c=-2a.
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    (Original post by Smaug123)
    What you have is a system of two equations in three variables. That means it's underdetermined: the solutions, if they exist, are not unique. You've reduced them to their simplest form, such that given a, you can produce a solution (a,b,c) = (a,a,-2a); that's the best you can do.

    That is to say, the solution to the system is precisely b=a, c=-2a.
    Oh right, it's just the lecturer came up with the answers:
    a=1, b=1 and c=-2
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    (Original post by SecretDuck)
    Oh right, it's just the lecturer came up with the answers:
    a=1, b=1 and c=-2
    (1,1,-2) is indeed a solution; indeed, in \mathbb{R}^3, the set of solutions is precisely those elements on the line spanned by the vector (1,1,-2).
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    (Original post by Smaug123)
    (1,1,-2) is indeed a solution; indeed, in \mathbb{R}^3, the set of solutions is precisely those elements on the line spanned by the vector (1,1,-2).
    Yes, the answer is supposed to be an orthogonal complement to a matrix. Thank you
 
 
 
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