- #1

Idioteqnician

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## Homework Statement

P5 is an inner product space with an inner product. We applied the Gram Schmidt process to the basis {1,x,x^2,x^3,x^4} and obtained the following result. {f1,f2,f3,f4,x^4+2}

What is the orthogonal complement of P3 in P5 with respect to this inner product?

## Homework Equations

http://tutorial.math.lamar.edu/Classes/LinAlg/OrthonormalBasis.aspx

has everything on the gram schmidt process

Definition of orthogonal complement:

Suppose that W is a subspace of an inner product space V. We say that a vector u from V is orthogonal to W if it is orthogonal to every vector in W. The set of all vectors that are orthogonal to W is called the orthogonal complement of W.

## The Attempt at a Solution

I'm not really sure. I feel like I need a defined inner product to actually find which vectors are orthogonal. I feel like I need to do something with the x^4+2, but honestly I am entirely lost.