Answer each of the statements that follow as true or false. In each case, explain or prove your answer.
Let {u1, u2}, {v1, v2}, and {w1,w2}, be bases for R2. If X is the transition matrix corresponding to a change of basis from {u1, u2} to {v1, v2} and Y is the transition matrix corresponding to a change of basis from {v1, v2} to {w1,w2}, then Z = XY is the transition matrix corresponding to the change of basis from {u1, u2} to {w1,w2}.
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