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Math Help - Textbook Statement Is Confusing

  1. #1
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    Textbook Statement Is Confusing

    Hi,

    This is a page from a text book I am reading:

    Textbook Statement Is Confusing-aem_2.2_53.png

    I can't figure out what the line "(3) and (4) will be basic ..." means. In particular what they mean by "basic".

    Any help is very appreciated.

    Scott.
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  2. #2
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    \displaystyle e^{\lambda x}\neq 0. Thus, the characteristic equation holds the only values that will make the equation 0.

    \lambda^2+a\lambda+b \ \mbox{is a quadratic equation which is solved from factoring or the quadratic equation} \ \lambda=\frac{-a\pm\sqrt{a^2-4(1)(b)}}{2(1)}
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  3. #3
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    Thank you, that pushed me in the right direction.

    I was thinking basic and basis were related so there was some relation to linear independence. But basic means non-zero variable in the Operations Research sense.
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