Proving Basis of Av with Invertible A Matrix

  • Thread starter Thread starter Chris Rorres
  • Start date Start date
  • Tags Tags
    Basis Matrix
Chris Rorres
Messages
4
Reaction score
0
If A is an invertible matrix and vectors (v1,v2,...,vn) is a basis for Rn, prove that (Av1,Av2,...,Avn) is also a basis for Rn.
 
Physics news on Phys.org
Hi Chris! :wink:

Show us how far you get, and where you're stuck, and then we'll know how to help! :smile:
 
why don't threads like this get moved to homework?
 
Just lazy mentors!
 
I need to prove that (Av1,Av2,...,Avn) spans and that it is linearly independent but this proof is so confusing to me that i don't even know where to start doing that.
 
You need to show that b* A(v_1) + ... b_n A(v_n) = 0 implies b_1 ... b_n equals zero, right? Well, you know since A is invertible, what is it's kernal?
 

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

Proving the Basis Property of S' for Rn Using Invertible Matrices
Replies
17
Views
3K
Why are all the singular values of A equal to 1?
Replies
9
Views
3K
Change of basis to express a matrix relative to a set of basis matrices
Replies
4
Views
2K
I Getting eigenvalues of an arbitrary matrix with programming
Replies
1
Views
2K
Prove B is invertible if AB = I
Replies
40
Views
5K
Matrix representation of a linear mapping
Replies
6
Views
2K
How Does Orthogonality and Matrix Transformation Affect Vector Spaces?
Replies
1
Views
5K
Prove Linear Independence of {[w1]s, [w2]s,...,[wk]s} in V
Replies
2
Views
2K
Prove there does not exist invertible matrix C satisfying A = CB
Replies
6
Views
2K
Find matrix corresponding to Linear Tranformation (Orth. Projection)
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top