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## Homework Statement

Let x be a fixed nonzero vector in R^3. Show that the mapping g:R^3→R^3 given by g(y)=proj

_{x}y is a linear operator.

## Homework Equations

proj

_{x}y = [itex]\left(\frac{x\cdot y}{\|x\|}\right)x[/itex]

My book defines linear operator as: Let V be a vector space. A linear operator on V is a linear transformation whose domain and codomain are both V.

## The Attempt at a Solution

I know how to show g is a linear transformation but I need help proving that g is a linear operator. Do I need to show y and proj

_{x}y share the same vector space? If so, how would I go about doing that?

Thanks