Problem

Let X be a square matrix that has the form where A and D are square matrices an...

Let X be a square matrix that has the form

where A and D are square matrices and A⁻¹ exists. It is known that X⁻¹ exists if and only if (D − C A⁻¹B)⁻¹ exists. Verify that X⁻¹ is given by

As an application, compute the inverse of the following:

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Solutions For Problems in Chapter 8.1

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