Hi, All: This is a post from another site that was interesting but was not answered: can I reasonably > argue that three planes in 3-space are not likely > to intersect at a point using the fact that >t GL(3,R); > the subset of invertible 3x3-matrices has measure 0 > in M(n,R); the set of all 3x3-matrices? > > Basically, the intersection of three planes Pi:= > > a_ix+b_iy+c_iz =d_i ; i=1,2,3. > > Is the same as having the matrix M with rows > (a_i b_i c_i ) can be reduced to Jordan form > with all 1's on the diagonal, and this is the > same as M being invertible. i.e., if M is invertible, then it can be turned into the Jordan Form as the identity, which means that Ax=b will have a solution, with b=(d_1,d_2,d_3) as above, i.e., the d_i are the constant terms. Seems reasonable; wonder what others think.