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Math Help - for which values of k the system has infinite number of solutions ?

  1. #1
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    for which values of k the system has infinite number of solutions ?

    Hello,

    I have a small question, I am not sure about it.

    I had a system of linear equations. I was asked for which values of k, the system has infinite number of solutions, with 2 degrees of freedom.

    The degrees of freedom thing kind of confused me, usually I know how to approach these things.

    I have eliminated the system, the attached photo contains the matrix of the system (including the vector B as last column) after I eliminated it in the Gausian way.

    What do I do now ? What's with the degrees of freedom ?

    if I didn't have the degrees of freedom condition I would say k=2....does it change the answer ?
    Attached Thumbnails Attached Thumbnails for which values of k the system has infinite number of solutions ?-matrix.jpg  
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  2. #2
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    Re: for which values of k the system has infinite number of solutions ?

    Degrees of freedom? Is this statistics?

    If k = 2, like you said, we have a row of all 0.

    What does that tell you?

    Spoiler:

    It should say you have a free variable.
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