Suppose B = {b1, ..., bn} is a basis for a vector space V. Which of the below is/are not true?

Module 18: question 1 . Suppose B = {b,. ..., b,, } is a basis for a vector space V. Which of the below is/ are not true? A For every vector x in V, there exists a unique set of scalars c. ..., C,, (weights), such that x = c, b, +...+c,,b,. B The existence of the set of scalars c,. ...,c,, in choice A follows from the property that V = Span(bj, ..., b.]. The uniqueness of the set ci, ....ca in choice A follows from the property that the set B = (b,,..., b,,} is linearly dependent. D The vector of weights (cj, ..., co) defined in choice A is called the B-coordinate vector of x and denoted [x] B. E The mapping x - [x]: from a vector space V to R" is called the coordinate mapping (determined by the basis B). The B-coordinate vectors of b,, ..., b,, in the basis B are undefined. If x is in R" and E = (e,, ...,e,, } is the standard basis for R", then [X]E= X