Question

Prove that vectors u , v and w are coplanar if and only if vectors u , v and w are linearly dependent.

Answer 1

Coplanar vectors will be in R^2. If a subspace of R^n contains more than n vectors, the vectors are linearly dependent by a theorem you can find at this web page < http://www.math.vanderbilt.edu/~msapir/msapir/mar1.html3 >.
Look for "If a subset S of Rn consists of more than n vectors then S is linearly dependent" and there is a link by it that will show you a proof.

Answer 2

It says the link is unavailable

Answer 3

oh well that's not good. one second

Answer 4

http://www.math.vanderbilt.edu/~msapir/msapir/mar1.html
my bad.

Answer 5

So this is the proof I need to use: http://www.math.vanderbilt.edu/~msapir/msapir/prlinindep.html

Answer 6

Does it make sense to you? I think part (1) should suffice. I feel like there's an easier way to prove it, but I don't have my notes with me. You could also show that an augmented matrix of 3 vectors that each have 2 terms will always row reduce to something that shows linear dependence.

Answer 7

I don't know if I'm making any sense right now.