Linearly Dependent Vectors: u,v,w

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Homework Help Overview

The discussion revolves around the concept of linear dependence among vectors u, v, and w, particularly in the context of a given equation involving scalar multiples of these vectors.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of the equation au + Bv + yw = a'u + B'v + y'w under the condition that a = a'. There are questions about the validity of the statement regarding linear dependence and the assumptions about the scalars B and B'.

Discussion Status

There is an ongoing examination of the original assertion about linear dependence, with some participants questioning the correctness of the claim and others suggesting that the given conditions do not provide sufficient information about the vectors involved. The discussion is active with various interpretations being explored.

Contextual Notes

Participants note potential confusion arising from the choice of letters used for scalars, suggesting that clearer notation could aid in understanding the relationships between the vectors and scalars.

sana2476
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If au + Bv + yw = a'u +B'v+y'w and a=a', then u,v,w are linearly dependent
 
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wait 1 second, can you show us your work?

B does NOT= to B'
 
The only thing that's given is the fact that a=a'...im guessing that would mean B=B' but I am not sure
 
This is NOT a tutorial so I am moving it to Homework.

And "If au + Bv + yw = a'u +B'v+y'w and a=a', then u,v,w are linearly dependent"
is certainly NOT true. Take B= B'= y= y'= 0. The condition is simply that au= au which tells us absolutely nothing about u, v, w.
 
sana2476 said:
If au + Bv + yw = a'u +B'v+y'w and a=a', then u,v,w are linearly dependent
As a side note, it would be helpful for you to be consistent with the letters you use. How did you happen to pick a, B, and y?

Apparently u, v, and w are vectors, so it would be good to use letters for scalars that won't be confused as vectors, say a, b, and c, or c1, c2, and c3.
 

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