In general, the eigenvalues of a diagonal matrix are given by the entries on the diagonal. verify this for 2 × 2 and 3 × 3 matrices.

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Atown has a population of 17000 and grows at 2.5% every year. to the nearest year, how long will it be until the population will reach 19600?