Completeness of a set of basis vectors in 3D Euclidean space.

bossman007
Messages
60
Reaction score
0

Homework Statement



The problem is Exercise 2 in the picture

[PLAIN]http://postimage.org/image/3ou3x1sh7/ [/PLAIN]

Homework Equations



The hint says: can you express and three-dimensional vector in terms of just two linearly independent vectors?

The Attempt at a Solution



I have no idea where to begin...
 
Last edited by a moderator:
Physics news on Phys.org
does this have to do with gram-schmidt processes? Any tips on just how to begin? I find my hint very confusing because this is a meth methods in physics class that moves at a pace faster than an F1 fighter jet :(
 
What is the dimension of Euclidean three-space? What is the definition of dimension?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Dot product and basis vectors in a Euclidean Space
Replies
4
Views
2K
Null space of dual map of T = annihilator of range T
Replies
1
Views
2K
Dimension statement about (finite-dimensional) subspaces
Replies
15
Views
1K
Components of a vectors with respect to basis are unique?
Replies
4
Views
3K
T/F: Subset of a spanning set always forms a basis
Replies
3
Views
2K
Proving That Any Vector in a Vector Space V Can Be Written as a Linear Combination of a Basis Set
Replies
3
Views
1K
Help with linear algebra: vectorspace and subspace
Replies
15
Views
3K
Vector space of functions from finite set to real numbers
Replies
17
Views
4K
I Definition of tangent vector on smooth manifold
Replies
21
Views
3K
Basis for the space of solutions (ODE)
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top