vector space algebra

[Abhishek Bandiya]

if u, v and w are three linearly independent vectors belonging to vector space G,, then for some scalars c1, c2 and c3, of which atleast 1 is non zero,, can we say that


c1.u+c2.v+c3.w =\0

 

[Deleted member 4993]

if u, v and w are three linearly independent vectors belonging to vector space G,, then for some scalars c1, c2 and c3, of which atleast 1 is non zero,, can we say that


c1.u+c2.v+c3.w =\0

Looks like you are stuck in the begining.

Let's start with definition/properties.

What are vectors and what are their properties?

Under what condition/s u, v and w would be called linearly independant vectors?

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Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[HallsofIvy]

if u, v and w are three linearly independent vectors belonging to vector space G,, then for some scalars c1, c2 and c3, of which atleast 1 is non zero,, can we say that


c1.u+c2.v+c3.w =\0

This follows immediately from the definition of "independent". Can you state that definition?