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Suppose that u1, u2, . . . , ut are vectors in Cn (complex number) which are linearly independent.
(a) Also suppose that "M" is an n x n matrix that is invertible. Show that Mu1, Mu2, . . . , Mut are linearly independent vectors.
(b) This isn't true when "M" is not invertible. Find a counterexample, as follows. Give an example of a 2 x 2 matrix "M" and two independent vectors u1, u2 Є C2 so that Mu1 and Mu2 are dependent.
This provides an example of working with linearly independent vectors and an invertible matrix.