"Greg Heath" <firstname.lastname@example.org> wrote in message <email@example.com>... > >>A1= round(rand(1,5)) > A2 = 1-A1 > A = [ A1 ; A2 ] > Why isn't rankA = 1? - - - - - - - - - For A1 and A2 to be linearly dependent requires that there exist two real or complex numbers, c1 and c2, not both zero, such that c1*A1 + c2*A2 = 0. The equality A2 = 1-A1 doesn't qualify for that. In fact A1 and A2 are linearly independent since no such c1 and c2 exist. Hence the rank of A must be 2.
Another way to see this is that the rank is the size of the largest square submatrix within A whose determinant is nonzero. Clearly this is 2.