1. The problem statement, all variables and given/known data Let A be the following 3 × 3 matrix: A =([4 2 6],[2 1 3],[2 1 3]) i) Find the rank of A ii) Show that there exists an 3 × 2 matrix W, of rank 2, such that AW = 0. iii) Construct one such matrix W. 2. Relevant equations 3. The attempt at a solution I think the answer to part 1 is rank(A)=1 since row 2 and row 3 are the same and row 1 is just twice row 2 or twice row 3. So there is only one independent row. I'm not sure how to prove the existence of W however. Do I use the rank-nullity theorem in some way? i.e. rank(a)+nullity(a)=n where A is a mxn matrix. In this case the nullity(A)=1. Any help would be much appreciated.