Are items a through e in the following list algorithms? If not, what qualities required of algorithms do they lack?

a. Add the first row of the following matrix to another now whose first column contains a nonzero entry. (Reminder. Columns run venicanx rows run horizontally.)

b. In order to show that there are as many prime numbers as them are natural numbers, match each prime number with a natural number in the following manner. Create pairs of prime and natural numbers by matching the first prime number with I (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 arc 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 'd 1%/1 ual products together to derive the dot product.

d. Lynne and Calvin arc trying to decided who will take the dog for a walk. Lynne suggests that they flip a coin and pulls a quarter out of maherypocbeketwcighCatledvin (dcaninotng that ititLinynign: tanf. and suspects that the quarter 4 or 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 1 will walk the dog.

3. If the outcome is tails on the first flip, and meads on the then you will walk the dog. second.

1 2 0 41 47 0324 3 10 22 3 4 2 L12 4