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Math Help - Equation to solve, anyone?

  1. #1
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    Equation to solve, anyone?

    Solve the equation 5x - ||v|| v = ||w||(w-5x) for x with v = (1, 2, -4, 0) and w = (-3, 5, 1, 1 )
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Equation to solve, anyone?

    so you have  ||v|| = \sqrt{1^2 + 2^2 + 4^2 + 0^2} = \sqrt{21} and  ||w|| = \sqrt{9 + 25 + 1 + 1} = \sqrt{36} = 6
     5x - \sqrt{21}v = 6w - 30x [
     35x = 6w + \sqrt{21} v
    right side equals  \begin{bmatrix}-18 + \sqrt{21} \\ 30 + 2 * \sqrt{21} \\ 6 - 4*\sqrt{21} \\ 6 \end{bmatrix}
    multiply the right side by  \frac{1}{35}
    and that is your x.
    x =  \frac{1}{35} \begin{bmatrix}-18 + \sqrt{21} \\ 30 + 2 * \sqrt{21} \\ 6 - 4*\sqrt{21} \\ 6 \end{bmatrix}
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