Having trouble with this linear algebra question not sure how to show what thier asking it says.

Let S be the vector space of (forward) signals, S consits of signals = infinte sequences s=(sn)n belongs to N = (s0,s1,...) and that addition and scalar multipcation is done as for vectors in Rn

(a)

Blips are special signals. They have value 1 at exactly one n and are silent otherwise. Thus, the ith blip is the signal b^(i)=(b^(i)n) n belong to N for which b^i(n)=0, and b^i(n)=1 Show that the finite collection of blips is linearly independent (Ti simplify the notation, you can show that for every natural number N the set of blips {b^1,b^2,...,b^(N)} is L.I!
pleae any help would be appreciated i need explnanations!

(b) Your reciever cuts off a signal s=(sn) at s1000. Hence it acts like the function R:S--->R^1000 given by R(s)=(sn)0<=n<=999 Show that R is a linear map

(c) The completely lost signals are the signals s=(sn) for which sn=0 for 0<=n<=999. Show that your reciever is loosing a lot, ie. show that the set of completely lost signlas is an infinte dimensional space?? whats that!