1. anonymous

let V be the space of polynomial over R $\le2$

2. anonymous

.let $\emptyset _{1} \emptyset _{2} \emptyset _{3}$ be the linear functional on V defiend by

3. anonymous

$\emptyset _{1}(f(t))=f(t)dt,\emptyset _{2}f(t)=f \prime (1),\emptyset _{3}(f(t))=f(0). here f(t)=a+bt+ct^2$ and f'(t) denots the derivative of f(t).

4. anonymous

find the basis {$f _{1}(t),f _{2}(t),f _{3}(t)$ of V that is dual to $\emptyset _{1}, \emptyset _{2}, \emptyset _{3},$

5. anonymous

6. anonymous

@zzr0ck3r

7. anonymous

@oldrin.bataku

8. anonymous

@Loser66

9. anonymous

@Michele_Laino

10. anonymous

@Kainui

11. anonymous

@oldrin.bataku

12. zzr0ck3r

Can you tell me what a basis, functional, and what do you mean by spaces, and over R. If you ant answer all four of those questions, you should read up before trying this.

13. anonymous

@jtvatsim

14. jtvatsim

OK, so I noticed that zzr0ck3r had some questions for you. Were you clear on those definitions?

15. jtvatsim

Phew... that was tough. I hope it isn't so tough reading it. Take your time through it. Ultimately, dual just means that you will be setting equations equal to 0s and 1. It's a simple idea, but very hard to get across. Good luck! I'm signing off for tonight. :)

16. jtvatsim

Not sure if the attachment went through, here is is again.