Question: The question is below _ True or False? Half of the following statements are true, and half are false. Pick one true statement. and provide

The question is below

_ True or False? Half of the following statements are true, and half are false. Pick one true statement. and provide a proof. Pick one false statement. and provide an explicit counterexample. (e) Let A be an m x 11 matrix and B be an n. x 1: matrix. If the columns of A8 are linearly independent, then the columns of B are linearly independent. (b) Let A be an n x 11 matrix, and suppose that B is obtained from A by performing 1': row operations on A. If det(B) = 2det(A]. then it = 1. (c) Let A and B be u x 1: matrices. If rank{AB') = n, then the linear transformation T : R" !- R\" dened by Thur) = A8): is one-to-one. ((1) HA is any or x :1 matrix, then dimNul(A] = dimNull'ATl

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