Question: Concern a vector space V, a basis B = {b 1 ,...,b n ), and the coordinate mapping x [x] B . Show that

Concern a vector space V, a basis B = {b1,...,bn), and the coordinate mapping x ↦ [x] B.

Show that the coordinate mapping is one-to-one. Suppose [u]B = [w]B for some u and w in V, and show that u = w.]

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