Let A = [A1 A2 the following statements are equivalent: An] be a matrix of ordernx n, this is, the column vectors A; E R". Show that (a) The system of linear equations Ax 0 has a unique solution (b) The set B = {A1, A2,... , An} is linearly independent. In other words, A is nonsingular if and only if B is linearly independent.

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