(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In R^4 which of the following sums U+V, U+W and V+W are direct? Give reasons

And which of these sums equal R^4?

2. Relevant equations

U = {(0, a, b, a-b) : a,b ∈ R}

V = {(x, y, z, w) : x=y, z=w}

W = {(x, y, z, w) : x=y}

3. The attempt at a solution

I put that none are direct sums as U is the only one to contain the zero vector meaning that none of the intersections would also be able to contain the zero vector. Is this right? It seems too simple.

For the second part I am unsure where to start.

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# Direct Sum of vectors

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