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## Homework Statement

A set of functions, F, is given below. Determine the size of the largest subset of F which is mutually orthogonal on the interval [-1, 1], and find all such subsets of this size. Show all of your work.

F = { 1, x, x

^{2}, sin(x), cos(x), cosh(x), sinh(x)}

## Homework Equations

Not really any relevant equations, but I am aware that for a function to be orthogonal on symmetric bounds, the integral of the product of the functions on those symmetric bounds must be equal to 0.

## The Attempt at a Solution

I have yet to complete an attempt because I'm not quite sure how to start. Any help would be appreciated.

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