Recent content by seyma

yeah sorry i forget to write empty

Let (X,d) be a metric space A and B nonempty subsets of X and A is open. Show: A\capB = \oslash Iff A\capB(closure)= empty Only B closure it is easy to show rigth to left but how can i use A's open property I try to solve with contradiction s.t. there exist r>0 Br(p)\subseteqA\capB(closure) but...

I want to show that the set of points (p,q) on the plane with rational coordinates p and q is countable. I proved set of rational numbers is countable by drawing table and I find (http://web01.shu.edu/projects/reals/infinity/proofs/combctbl.html ) Combining Countable Sets. However, I cannot put...

Homework Statement I have a trouble in this proof; Let A be an m\timesn matrix and B n\timesm matrix. If m\neqn show that at least one of the matrices AB and BA is singular. Homework Equations If it is singular not invertible and det=0 but how can I apply this question? The Attempt...

edit: A=A^T It must satisfies the operations in S and it requires that it must be closed under vector addition and scaler multiplication. I got it: symmetic matrix satisfies those condition :) thanks:)

My question is; Let S = {A € Mn,n | A = AT } the set of all symmetric n × n matrices Show that S is a subspace of the vector space Mn,n I do not know how to start to this if you can give me a clue for starting, I appreciate.