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## Use matrix A in Problem 2.6 and let Find D 1 A and AD 2 , thus illustrating (2.29) and (2.30)….

Use matrix A in Problem 2.6 and let

Find D1A and AD2, thus illustrating (2.29) and (2.30).

Problem 2.6

Let

(a) Find AB and BA.

(b) Find B + C, AC, and A(B + C). Compare A(B + C) with AB + AC, thus illustrating (2.15).

(c) Compare (AB)’ with B’ A’, thus illustrating Theorem 2.2b.

(d) Compare tr(AB) with tr(BA) and confirm that (2.87) holds in this case.

(e) Let a’1 and a’2 be the two rows of A. Find  and compare with AB in part (a), thus illustrating (2.27).

(f) Let b1 and b2 be the two columns of B. Find (Ab1, Ab2) and compare with AB in part (a), thus illustrating (2.28).

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