Question

Let u,v,w be vectors in R5. explain why there must be non-zero vectors orthogonal to u,v,w

Answer 1

You have to find s=(a,b,c,d,e} that is orthogonal to u, v, w, you will have to solve
3 equations in 5 unknowns. You can take a=1 and b =2 and you will be able to solve for
b,c,d and you are done,

Answer 2

You have to do some thinking to achieve that.

Answer 3

It is easy if u,v and w are linearly independent, here you are assured to find solutions for
b,c,d

Answer 4

If they are not, then they span a subspace of R^5 of dimensions less that 3. If w is a linear combinations of u and v, then find a vector perpendicular to u and v, hence it will be perpendicular to w.

Answer 5

ok thanks for your help. Ill look into it later today!

Answer 6

YW