Nullspace Definition and 58 Threads

Hey. I am doing some last minute exam study and came across this question: let A and B be nxn matrices. Prove that Null(AB) \geq Null(B) Now i think i did it correctly, but i wasn't sure if i perhaps overlooked something and there is a flaw in my proof. I began by stating that if any...

[SOLVED] Dimensionality, Rangespace & Nullspace Problem Homework Statement Prove (where A is an n x n matrix and so defines a transformation of any n-dimensional space V with respect to B, B where B is a basis of V) that \dim(R(A) \cap N(A)) = \dim R(A) - \dim R(A^2) The attempt at a...

Hello everyone I'm confused if I'm setting these equations up right: i have: 1 0 1 0 1 -2 0 0 0 so i said: x + z = 0; y - 2z = 0; z = ? because its a whole row of 0's, so u have no info about what z could be so i said let z = a; x + a = 0; y -2a = 0; z = a; x = a; y = 2a; z = a; so let a =...

Hello everyone, I think i did this right, but i want to make sure this is what they want. The questions says: In each case find a basis for and caclulate the dimension of nullA: Here is my work and problem! http://img207.imageshack.us/img207/2948/lastscan6ib.jpg I just found out its...

Hello everyone... I have the following matrix: A = -1 -4 1 7 -9 0 10 3 -3 -9 1 2 I can't row reduce this sucker! This isn't an agumented matrix i don't think, so i can't just take the square matrix and then find the inverse and mutliply it by vector b to find the values of a, b, c, d; So...

Hello everyone, it's final's time next week :cry: , so I will be posting here more often than usual :biggrin: Here is one problem I came across when doing review: The nullspace of non-zero 4x4 matrix cannot contain a set of 4 lin. indep. vectors. (T/F) The way I was thinking is that...

I'm not sure if I am making a mistake, or my book is wrong, or if both answers are correct. But, it is confusing me, and I would like to know why. We are asked to find the basis of the following subspaces on the matrix A. Find: R(A^T),\,\,N(A),\,\,\,R(A),\,\,N(A^T) I'm having trouble...

Nullspace and Orthogonal Complement Quick question: is the nullspace the orthogonal complement of the column space or the the row space? Thanks, sorry I don't have my textbook nearby.