Hi, I was wondering if someone could check my work for this linear algebra problem. I have attached the problem statement in the file "problem" and my work in the file "work." I would type out my work on here, but I couldn't figure out how to put matrices in a post so I just took a pic of my work. I only attached the work for proving S is a subspace. I basically checked the 3 conditions my professor gave me to determine if something is a subspace. They are (with respect to my problem): 1. Is the 0 vector in S? 2. If U and V are in S, is U+V in S? 3. If V is in S, then is cV in S for some scalar c? I feel like I made this problem too complicated. It took me a whole page to just prove S is a subspace. Can someone verify if that's accurate? Is there a faster way to do it or a way that takes up less paper?