Homework Statement
Find an orthogonal basis for the nullspace of the matrix
[2 -2 14]
[0 3 -7]
[0 0 2]
Homework Equations
The Attempt at a Solution
The nullspace is x = [0, 0, 0], so what is the orthogonal basis? It can be anything can't it?
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.