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Math Help - matrix solution and calculator input

  1. #1
    Jan 2011

    matrix solution and calculator input

    how can i state the following condition l^2 + m^2 + n^2 = 1 into the following matrix

    [-56.8 -55 -75] [l] =0
    [-55 -121.8 33] [m] =0
    [-75 33 -261.8] [n] =0
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  2. #2
    MHF Contributor

    Apr 2005
    If the determinant of that matrix is not 0, you can't- that matrix equation has a single solution which may or may not satisfy that additional condition. If the determinant is 0 (I haven't checked but I imagine that's why you are asking) then probably the best thing to do is to go ahead and "try" to solve the equation- since the determinant is 0, you won't be able to find a single solution but will be able to reduce to either a single equation in l, m, and n (if the matrix has rank two) or two equations relating them (if it has rank 1). In the first case, you can include your constraint with the single equation to get a one parameter solution, in the second, you can add it to the two equations to get three conditions that you can solve for a specific point (since that constraint is quadratic, there may be no solution).
    Last edited by HallsofIvy; January 26th 2011 at 05:52 PM.
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  3. #3
    A Plied Mathematician
    Jun 2010
    CT, USA
    The determinant is nonzero: I get -20.032. That means the only solution is the trivial solution (l,m,n) = (0,0,0), which cannot satisfy the condition of being on the unit sphere, as HallsofIvy mentioned.
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