16. Which of the following statements is false? (a) Let S = {v1, v2, . ....

16. Which of the following statements is false?

(a) Let S = {v1, v2, . . . , vm} be a subset of a vector space V with dim(V) = n. If m > n, then S is linearly dependent.

(b) If A is an m × n matrix, then dim Nul A = n.

(c) If B is a basis for some finite-dimensional vector space W, then the change of coordinates matrix PB is always invertible.

(d) dim(R17) = 17.

(e) If B1 and B2 are both bases for the same vector space, then B1 and B2 have the same number of vectors.

Expert Solution

Colby Messinger answered 2 years ago

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