Could someone please tell me how to answer the questions a, b and c? I really don't know where to start, since the matrix P is not given... Thanks for your help!
Let P be any invertible 3 x 3 matrix and define the matrix C as: C = PB
(a) Considering the relationship between B and C, what can you say about Nul(C)?
(b) What about Col(C)?
(c) What about Row(C)?
In answering the above questions, note that your statements must be valid for all invertible 3 x 3 matrices P (and not just for a particular choice of P). You should address the dimensions of the spaces and whenever possible you should say something about the spaces themselves, comparing those of C to those of B.