- #1
Chris Rorres
- 4
- 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.
Proving Basis of Av with Invertible A Matrix
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Homework Help Overview
The discussion revolves around proving that the set of vectors (Av1, Av2, ..., Avn) forms a basis for Rn, given that A is an invertible matrix and (v1, v2, ..., vn) is a basis for Rn.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants discuss the need to demonstrate that the new set of vectors spans Rn and is linearly independent. There is mention of confusion regarding how to initiate the proof.
Discussion Status
Some participants have offered guidance on the necessary steps to show linear independence and spanning, while others express uncertainty and seek clarification on the proof process. Multiple interpretations of the proof requirements are being explored.
Contextual Notes
There is an indication of confusion regarding the proof's complexity, and participants are questioning the clarity of the problem setup and the definitions involved.
- #2
tiny-tim
Science Advisor
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Hi Chris! 
Show us how far you get, and where you're stuck, and then we'll know how to help!
Show us how far you get, and where you're stuck, and then we'll know how to help!
- #3
ilia1987
- 9
- 0
why don't threads like this get moved to homework?
- #4
HallsofIvy
Science Advisor
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Just lazy mentors!
- #5
Chris Rorres
- 4
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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
Quantumpencil
- 96
- 0
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?