Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: What am I missing?
Posted:
Nov 22, 2012 6:18 PM


"Greg Heath" <heath@alumni.brown.edu> wrote in message <k8m4qf$8de$1@newscl01ah.mathworks.com>... > >>A1= round(rand(1,5)) > A2 = 1A1 > 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 = 1A1 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.
Roger Stafford



