(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define linear functionals l_{k}on P_{n}by

l_{k}(p) = p(t_{k})

Show that the l_{k}are linearly independent.

2. Relevant equations

q_{1}(t)= (t-t_{2})(t-t_{3})...(t-t_{n})

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Linear Algebra(functionals, linear independence)

Can you offer guidance or do you also need help?

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