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Linear Algebra : Symmetric Polynomials and Inner products

Let be the real vector space of "symmetric" polynomials of degree at most 4, with inner product

a. find a basis for V and determine dim V.
b. viewing V as a subspace of R) with the same inner product, find the "closest" point in V to the polynomial .

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COMMENT FROM STUDENT:
from your solution..You noted that
To minimize the above expression, we can minimize ||g1(x)||^2 to 0 by setting a=c=0.
why do we set a=c=0?? is it just because to minimize???
or it has to be 0??
what if we choose ...

Solution Summary

Symmetric Polynomials and Inner products are investigated.

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