This stuff is confusing. I don't know if it's hard or not, I just have a feeling I don't really know what I'm doing. 1. The problem statement, all variables and given/known data 1. Show that the equation Ax=b has a unique solution if and only if the solution to Ax=0 is x=0. 2. Let A be an m x p matrix, and let B be a p x n matrix. Show that the range of A is contained in the range of AB. Show that the kernel of B is contained in the kernel of AB. Is the reverse inclusion true in either case? 2. Relevant equations 1. Ax=b; Ax=0; x=0 2. See below. 3. The attempt at a solution 1. I really have no idea what to do. 2. A=[v1 ... vp]; B=[w1 ... wn] AB=[Aw1 ... Awn] im(A)=c1v1 + ... + cpvp im(AB)=c1Aw1 + ... + cnAwn=A(c1w1 + ... + cnwn) That's all I have. This is probably not even close to what I'm supposed to be doing. Please help!