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Thread: Linear Equation

  1. #1
    MHF Contributor Jason76's Avatar
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    Linear Equation

    Definiton of a linear equation

    $\displaystyle a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b$ where $\displaystyle b$ is a real number

    Note if $\displaystyle b = 0$, it's a homogeneous equation.

    What are some reasons why these statements are true?

    $\displaystyle 3x - 4xy = 0$ - not linear

    $\displaystyle x^{2} + y^{2} = 4$ - not linear

    $\displaystyle (\sin2x) - y = 14$ linear
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  2. #2
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    Re: Linear Equation

    Quote Originally Posted by Jason76 View Post
    Definiton of a linear equation

    $\displaystyle a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b$ where $\displaystyle b$ is a real number

    Note if $\displaystyle b = 0$, it's a homogeneous equation.

    What are some reasons why these statements are true?

    $\displaystyle 3x - 4xy = 0$ - not linear
    the "xy" term cannot be written in the form "ax+ by" for any numbers a and b.

    $\displaystyle x^{2} + y^{2} = 4$ - not linear
    The terms $\displaystyle x^2$ and $\displaystyle y^2$ cannot be written in the form "ax+ by" for any numbers a and b.

    $\displaystyle (\sin2x) - y = 14$ linear
    sin(2x) cannot be written in the form "ax+ by" for any numbers a and b.
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