Cho ánh xạ f : R3 −→ R3, xác định bởi: f(x1, x2, x3) = (x1 − x2, x1 + x2 + 2x3, x1 + 2x2 + 3x3)
a) Chứng minh f là ánh xạ tuyến tính
b) Tìm ma trận của ánh xạ tuyến tính f đối với cơ sở
B = {u1 = (1, 2, 0), u2 = (1, 1, 0), u3 = (0, 0, 1)}
c) (∗) Tìm tập hợp các véc tơ v = (x1, x2, x3) sao cho f(v) = (3, 5, 6)

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297

To finance her community college education, sarah takes out a loan for $2900. after a year sarah decides to pay off the interest, which is 4% of $2900. how much will she pay

Sam opened a money-market account that pays 3% simple interest. he started the account with $7,000 and made no further deposits. when he closed the account, he had earned $420 in interest. how long did he keep his account open?