Question: Given A E Rnxn, B E Rnxm, C E Rmxn, D E Rmxm, a E R, and b E Rm. Assume D and (A -

Given A E Rnxn, B E Rnxm, C E Rmxn, D E Rmxm, a E R", and b E Rm. Assume D and (A - BD-'C) are invertible. Let X = A B 2 D 1. Give the expression of the solution to 2 B - [8] Also, give the expression of X-1. 2. Prove that det(X) = det(D)det(A - BD-'C)

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