Answer each of the following as True or False justifying your answers: a.)If A and B are n×n matrices, then (A+B)²=A²+2AB+B².
b.)If A is an n×n invertible symmetric matrix, then (A⁻¹ )^k is symmetric, for any positive integer k.
c.)Let A be an n×n matrix. If A is invertible, then |A|≠0.
d.)If A and B are n×n matrices, then |A+B^T |=|A^T+B|.
e.)The vectors (a,0,0), (1,a,0) and (2,3,a) in R³ are linearly independent for all a∈R.

Mr. vector door is buying two new cowboy hats all together the hats cost $75.12 the second heart cost twice as much as the first hat what is the price of the more expensive at round to the nearest hundredth

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

Monitors manufactured by tsi electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. if a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. round your answer to four decimal places.