Hi, I have a few questions on PS5.
1. S4.1 P9: I got the right blanks, but I don't understand why we can make the conclusion.
2. S4.1 P33: The solution doesn't show how to get nullspace and left nullspace. If {r1,r2} and {c1,c2} each contain linearly independent vectors, isn't the r=m=n, and therefore only zero vectors in nullspace and left nullspace (b/c no free variables)? How can {n1,n2} and {l1,l2} be non-zero vectors?
S4.2 P34: I get everything in the solution up until it says that AB is rxr. Shouldn't it be mxn? Even if A=B', AB=nxn. How can we say AB is rxr?
Thanks in advance!!

Question

Hi, I have a few questions on PS5.
1. S4.1 P9: I got the right blanks, but I don't understand why we can make the conclusion. 
2. S4.1 P33: The solution doesn't show how to get nullspace and left nullspace. If {r1,r2} and {c1,c2} each contain linearly independent vectors, isn't the r=m=n, and therefore only zero vectors in nullspace and left nullspace (b/c no free variables)? How can {n1,n2} and {l1,l2} be non-zero vectors?
S4.2 P34: I get everything in the solution up until it says that AB is rxr. Shouldn't it be mxn? Even if A=B', AB=nxn. How can we say AB is rxr?
Thanks in advance!!

anonymous · Answer

Could you clarify where these problems can be found, or better yet, post the original questions themselves?

danpak94 · Answer

All of the problems can be found on Strang's linear algebra course, assignments, problem set #5. I'm also attaching copies of the problem here.

cuimengmeng · Answer

hi,I have the same question with you. Thus,I think the answer should be dependent