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Math Help - Examine the consistence of the following eq

  1. #1
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    Examine the consistence of the following eq

    Question: Examine the consistency of the following system of equations:

    2x - 5y +7z = 6
    3x - 8y + 11z = 11
    x - 3y +4z = 3

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  2. #2
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    Quote Originally Posted by zorro View Post
    Question: Examine the consistency of the following system of equations:
    2x - 5y +7z = 6
    3x - 8y + 11z = 11
    x - 3y +4z = 3
    A linear system of equations is consistent if each of the equations have a common solution. So, we attempt to find a common solution  {x,y,z} that satisfies each equation in the following linear system:

     2x - 5y +7z = 6
     3x - 8y + 11z = 11
     x - 3y +4z = 3 .

    You can use substitution, linear combination, Gaussian elimination or whichever is your preferred method for solving a linear system of equations.
    Eventually, you will either get some solution {x,y,z} that satisfies the system of equations, or you will observe some ridiculous contradiction (i.e., 2=8) which is your cue that you have inconsistent equations of a linear system. Be sure to check your work. Holla back if you are still stuck.

    -Andy
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  3. #3
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    I am getting a Inconsistent equation as the Rank of A \ne Rank of C

    Is that correct?????
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  4. #4
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    You can write this system in matrix form:

    A\mathbf{x} = \mathbf{b}

    with

    A = \left[\begin{matrix} 2 & -5 & 7\\ 3 & -8 & 11\\ 1 & -3 & 4 \end{matrix}\right].


    Now find |A|. If it is nonzero, there will be a solution and the system will be consistent.
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  5. #5
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    but could u please tell me if my solution is correct or no ???
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    Well...

    |A| = 2\left|\begin{matrix}-8 & 11\\ -3 & 4 \end{matrix} \right| + 5\left| \begin{matrix} 3 & 11\\ 1 & 4\end{matrix}\right| + 7 \left|\begin{matrix}3 & -8\\ 1 & -3 \end{matrix}\right|

     = 2(-8 \cdot 4 - 11 \cdot -3) + 5(3 \cdot 4 - 11 \cdot 1) + 7[3\cdot -3 - (-8)\cdot 1]

     = 2\cdot 1 + 5 \cdot 1 + 7\cdot -1

     = 2 + 5 - 7

     = 0.


    So I would agree with your statement that the system is inconsistent.
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  7. #7
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    Thanks mite
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