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,...,b_n), and the coordinate mapping x ↦ [x] _B.

Show that a subset {u₁,...,u_p} in V is linearly independent if and only if the set of coordinate vectors {[u₁]_B,...,[U_p]_B} is linearly independent in Rⁿ.

+ Cpup = 0 The zero vector in V [Cu ++Cpup lg

+ Cpup = 0 The zero vector in V [Cu ++Cpup lg = [0] The zero vector in R" B B

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