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Unformatted text preview: (Partial) Solutions to Homework 5 For this homework, due to some requests, Ill give more solutions but less detail on how to think about things. Just the solutions. Problem 14.3: In computer science, the complexity of an algorithm is com- puted (roughly) by counting the number of times a given operation is performed. Suppose adding or subtracting any two numbers takes a seconds, and multiply- ing two numbers takes m seconds. Then, for example, computing 2 6- 5 would take a + m seconds. i. How many additions and multiplications does it take to compute the de- terminant of a general 2 2 matrix? ii. Write a formula for the number of additions and multiplications it takes to compute the determinant of a general n n matrix using the definition of the determinant. Assume that finding and multiplying by the sign of a permutation is free. iii. How many additions and multiplications does it take to compute the de- terminant of a general 3 3 matrix using expansion by minors? (Assume3 matrix using expansion by minors?...
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- Spring '10