Show that V{(J - M)VI is invertible. Answer: Since the columns of VI form a basis, then
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Show that V{(J - M)VI is invertible.
Answer: Since the columns of VI form a basis, then 0 = VI b iff b = O.
Also (I - M)Vlb = 0 iff Vlb E C(X), but Vib E C(X) iff b = 0 by choice of VI' Thus, (1 - M)Vlb = 0 iff b = 0; hence (I - M)VI has full column rank and V{(J - M)VI is invertible.
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