Let I denote the space of all infinite sequences of real numbers, where addition and scalar multiplication is defined componentwise: (a1, 22, ...) + (61, 62, ...) = (a1 + b1, 22+ b2, ...), a(a1, a2, ...) = (aa1, 002, ...), then this is a vector space (you do not have to verify this). Define the operators L, R: 1 7 by: L(a1, 22, 23, ...) = (a2, 23, 24,...), R(21, 22, 23, ...) = (0, 21, 22, ...), then these are linear operators on l. Do the following: i) Find the kernels of L and R. ii) Show that LOR=Id, but RoL #Id.

Consider the diagram. which line segment has the same measure as st? rx tx sr xs

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

What is the slope of (0,32) and (100,212)