- #1

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## Homework Statement

Let u,v,w be three linearly independent vectors in ℝ7. Determine a value of k,

k= , so that the set S={u-3v,v-5w,w-ku} is linearly dependent.

## Homework Equations

## The Attempt at a Solution

I don't really know why knowing that we're in ℝ7 will help. I know a couple of ways to solve this, but I don't think that they really apply. If we go:

A(u-3v)+B(v-5w)+C(w-ku)=0

[u-3v,v-5w,w-ku][A;B;C]=0

If it was square we could set the determinant equal to zero and solve for k. Otherwise, we have the matrix,

[u-3v,v-5w,w-ku,0]

If the matrix was little friendlier we could do some G-J elimination. Er... actually I'm not sure if that would help.

Any hints?

Thanks!