Given vectors u1,...,up, and w in V, show that w is a linear combination of u1,...,up if and only if [w]B is a linear combination of the coordinate vectors [u1]B,...,[up]B.
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.., Up. This means that there exist scalars a1, a2, ..., ap such that: W = a1*U1 + a2*U2 + ... + ap*Up Now, let's consider the coordinate vectors [W]s, [U1]s, [U2]s, ..., [Up]s. By definition, these are the coordinates of W, U1, U2, ..., Up with respect to some Show more…
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