Question

With refernce to the base (u, v, w) show that the vector u+w, -u+w, u+v+w also constitute a base.

Give the formula for the transformation of the coordinates of a vector.
Pls someone help me.

Answer 1

I assume you actually mean {u,v,w} is a BASIS. By definition, that means for any vector s in the vector space, there exists constants a,b,c, such that
s = au + bv + cw
that is, for an arbitrary vector s, it is possible to write s as a linear combination of u, v and w.

If you now what to show that these three other vectors are a basis, show how an arbitrary vector such as s can be written as a linear combination of them.

Answer 2

Thanx