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Let B be a nonsingular matrix and let A = BT - B (a) Show that A does not admit and LU decomposition. (b) Let T be a nonsingular matrix such that T'A admits an LU decomposition TA = LU i. Given a vector b E R", provide an algorithm to solve Ar = b in O(n2) operations ii. Compute the exact number of operations required to solve the previous system