Question: 7. Let A be a nonsingular matrix and D an arbitrary matrix, both square. Show that (a) the first two terms of the Taylor series

7. Let A be a nonsingular matrix and D an arbitrary matrix, both square. Show that (a) the first two terms of the Taylor series expansion of det(A + ED) is det (A + ED) = det(A) (1 + etr (A-'D) ) +e (b) the first two terms of the Taylor series expansion of (A + ED) are given by (A + ED) -1 = A-'(1+ EDA -] ) +e where tr denotes the trace and e is an error term involving terms of order e and higher

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