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## Homework Statement

Prove that the set of all 3-vectors orthogonal to [1, -1, 4] forms a subspace of R^3.

## Homework Equations

Orthogonal means dot product is 0.

## The Attempt at a Solution

I know the vectors in this subspace are of the form

[a,b,c] where a - b + 4c = 0.

However I don't know how to use this to show there is closure under vector addition and scalar multiplication.