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## Homework Statement

Define linear functionals l

_{k}on P

_{n}by

l

_{k}(p) = p(t

_{k})

Show that the l

_{k}are linearly independent.

## Homework Equations

q

_{1}(t)= (t-t

_{2})(t-t

_{3})...(t-t

_{n})

## The Attempt at a Solution

I really don't know where to start. I do have the following equation:

If the lks are linearly independent then there exits as such that

a1l1(k)+...+anln(k)=0 where all the as=0.

That's all I have. I don't see how can I can incorporate the hint given.