Hello everyone!! I'm alittle confused, my professor found the Null space after some students didn't get how to do it, such as myself. Here is the image and problem: http://img497.imageshack.us/img497/4161/lastscan9es.jpg [Broken] Thats the row reduced forum of the orginal matrix. The orginal matrix was: -1 4 1 7 -9 0 10 3 -3 -9 1 2 he added a column of 0's so it wuold make it a square matrix, then he row reduced to get the matrix in the link. I understand where the Null space of A is: 9/37 7/37 1 0 that makes sense to me, but then he adds in: d = 0 0 0 1 why is that also a set of vectors in the Null space? d is just all 0's, how can he have a 1 also? Then i'm lost on what i'm suppose to do to find the image space, you can see my work in the image above. What do i do after i set them equal to r,s,t,u? Thanks!