Linear Dependence of Three Functions. Three Functions y1(t) ,y2(t), and y3(t) are sa...

Linear Dependence of Three Functions. Three Functions y1(t) ,y2(t), and y3(t) are said to be linearly dependent on an interval I if, on I, at least one of these functions is a linear combination of the remaining two [e.g., if ]. Equivalently (compare Problem 33), y₁,y₂, and y₃ are linearly dependent on I if there exist constants C1,C2,and C3, not all zero, such that for all t in I. Otherwise, we say that these functions are linearly independent on I. For each of the following, determine whether the given three functions are linearly dependent or linearly independent on : (a) (b) (c) (d)