# Linear Algebra : Symmetric Polynomials and Inner products

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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.

Please see the attached file for the fully formatted problems.

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#### Solution Preview

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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 ...

#### Solution Summary

Symmetric polynomials and inner products are investigated in the solution.

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