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Thread: unique solutions to system of equations.

  1. #1
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    unique solutions to system of equations.

    I was under the impression that a system has a unique solution if its determinant was not equal to zero. This website seems to verify this fact https://math.oregonstate.edu/home/pr...em/system.html
    Below are the solutions my teacher has provided to the question. But who is right? Do you get a unique solution if you set the matrix equal to zero or do you get a unique solution if you set the matrix not equal to zero?

    unique solutions to system of equations.-question.png
    unique solutions to system of equations.-teacher-answer.pngClick image for larger version. 

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  2. #2
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    Re: unique solutions to system of equations.

    I agree with you. A linear system has a unique solution if the corresponding system-matrix has a non-zero determinant. I think your teacher implicitly means that the solution is given as the set:

    \mathbb{R} \setminus \lbrace -1 , -3 \rbrace
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  3. #3
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    Re: unique solutions to system of equations.

    Your teacher explicitly states the values of $k$ that you left implicit. But you never actually said in your answer what you think those values represent.

    It's not sufficient in solving a problem, to just scribble some lines. You should explain what you are doing and why, and clearly state your final result.

    Why did you transform the matrix like the anyway?
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  4. #4
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    Re: unique solutions to system of equations.

    This is not my work. This is my teachers solution to the question... I am just trying to understand it.

    Krisly, what does your notation mean in English?
    Last edited by thatsmessedup; Nov 19th 2017 at 12:19 PM.
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  5. #5
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    Re: unique solutions to system of equations.

    It means, the real numbers without the set consisting of -1 and -3. It is equivalent to say k can be anything except -1 or -3.
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