Basis proof

  • #1
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.
 

Answers and Replies

  • #2
tiny-tim
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Hi Chris! :wink:

Show us how far you get, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
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why don't threads like this get moved to homework?
 
  • #4
HallsofIvy
Science Advisor
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Just lazy mentors!
 
  • #5
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.
 
  • #6
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?
 

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