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Unformatted text preview: EECS 203 Homework 9 Solutions 1. (E) 3.8.24 (a) ( A 1 A 2 ) A 3 If we compute the product as A 1 ( A 2 A 3 ), then by the result of Exercise 23 it will take 50 10 40 multiplications for the first product and then 20 50 40 for the second. This is a total of 60,000 multiplications. If we compute the product as ( A 1 A 2 ) A 3 , then it will take 20 50 10 multiplications for the first product and then 20 10 40 for the second. This is a total of 18,000 multiplications. Therefore the second method is more ecient. (b) A 1 ( A 2 A 3 ) 2. (M) 3.8.22 A matrix is symmetric if and only if it equals its transpose. So let us compute the transpose of AA t and see if we get this matrix back. Using Exercise 17b and then Exercise 16, we have ( AA t ) t = ( ( A t ) t ) A t = AA t as desired. 3. (E) 8.1.6 bdfh Reexive Symmetric Antisymmetric Transitive (b) x = y Yes Yes No Yes (d) x = 2 y No No Yes No (f) xy = 0 No Yes No No (h) x = 1 or y = 1 No Yes No No 4. (E) 8.1.24 (a)...
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- Spring '07