Problem 4: Let F be any field. Let P, be the space of F-coefficient polynomials of degree


Problem 4: Let F be any field. Let P, be the space of F-coefficient polynomials of degree <n. Let<br>ro, ..,In be (n+1) distinct points in F. Show that for each set of (n+1) real numbers yo,., Yn;<br>there exists a unique polynomial p(r) e P, which interpolates the points (ro, Yo), . , (xn; Yn), ie.,<br>p(r;) = y; for each i.<br>(Hint: You can pretend F = R if you want to, but your argument will not use anything particular<br>about R. One of your previous homework problems on determinants is potentially helpful.)<br>

Extracted text: Problem 4: Let F be any field. Let P, be the space of F-coefficient polynomials of degree

Jun 05, 2022
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