Are items a through e in the following list algorithm? If not, what qualities required of algorithms do they lack? a. Add the first row of the following matrix to another row whose first column contains a nonzero entry. (Reminder: Columns run vertically; rows run horizontally.)
[1 2 0 4 0 3 2 4 2 3 10 22 12 4 3 4]
b. In order to show that there are as many prime numbers as there are natural numbers, match each prime number with a natural number in matching the first prime number with 1 (which is the first natural number) and the second prime number with 2, the third with 3, and so forth. If, in the end, it turns out that each prime number can be paired with each natural number, then it is shown that there are as many prime numbers as natural numbers.
c. Suppose you're given two vectors each with 20 elements and asked to perform the following operation. Take the first element of the first vector and multiply it by the first clement of the second vector. Do the same to the second elements, and so forth. Add all the individual products together to derive the dot product.
d. Lynne and Calvin are trying to decided who will take the dog for a walk. Lynne suggests that they flip a coin and pulls a quarter out of her pocket. Calvin does not trust Lynne and suspects that the quarter may be weighted (meaning that it might favor a particular outcome when tossed) and suggests the following procedure to fairly determine who will walk the dog.
1. Flip the quarter twice.
2. If the outcome is heads on the first flip and tails on the second, then I will walk the dog.
3. If the outcome is tails on the first flip, and heads on the second, then you will walk the dog.