or each setS deterimine whetherS iS Innearly independent and

or each setS, deterimine whetherS iS Innearly independent (and justiry your decision

Solution

S = {sin x , sin (x+1) , sin (x+2) }

the set is linearly independen if

c1sin x + c2 sin (x+1) + c3 sin (x+2) = 0

at any one value of x sin x , sin (x+1) , sun (x+2) is never = 0

such a value of x does not exists

the only solution for this equation is

c1 = c2 = c3 = 0

hence they are linearly independent