Question: (a) Let U be a m n matrix and V an n m matrix, such that the m m matrix I m

(a) Let U be a m × n matrix and V an n × m matrix, such that the m × m matrix I_m+ U V is invertible. Prove that I_n +V U is also invertible, and is given by

(b) The Sherman–Morrison–Woodbury formula generalizes this identity to

Explain what assumptions must be made on the matrices A,B, U, V for (1.42) to be valid.

(In + VU)= In - V(Im + UV)- U.

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