> From: Zach
>
> (The original problem was to find tuples of reals (n1, n2, m1, m2)
> such that n1*a1 + n2*a2 = m1*b1 + m2*b2 (where a1, a2, b1, and b2 are
2D vectors).)
Firstly, the solution is not unique. If (n1, n2, m1, m2) is a solution
then
so is (k*n1, k*n2, k*m1, k*m2).
Now write this as a matrix equation, where a1 = (a1x, a1y) and so on
[ a1x a2x -b1x -b2x ] [ n1 ] [ 0 ]
[ a1y a2y -b1y -b2y ] [ n2 ] = [ 0 ]
[ m1 ]
[ m2 ]
and solve as an underdetermined linear system. The nature of the
solution will depend
on the rank of the coefficient matrix.
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