problem is solved and done.

It was a rounding issue from the professor that caused a problem meant to have a free variable not to have it, right?

wat do u mean

^A solution doesn't exist as it is written, as we've shown. If the coefficients were slightly different (probably not rounded vs rounded) in the initial 3 linear equations, there would've been a free variable (REF form would have a row of zeros), so there would be infinitely many solutions to this system (i.e. the 3 planes would have met on an entire line instead of just a single point). Given this, that line would've hit the sphere at two places and exact solutions satisfying the sphere constraint would have existed.

This post was edited by Amaston on Sep 24 2015 06:15pm