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## Homework Statement

Find a basis for each of these subspaces of R4

All vectors that are perpendicular to (1,1,0,0) and (1,0,1,1)

**2. The attempt at a solution**

I'm not sure how to approach this question. The only thing I can think of is that a vector that would be perpendicular to both would be where the dot product would equal zero aye?

So then that would give me

1x1 + 1x2 = 1x1 + 1x3 + 1x4 = 0.

So in which case, I'd do RREF

[[1,1,0,0]

[1,0,1,1]]

to

[[1,0,1,1]

[0,1,-1,-1]]

I get stuck here because I'm not sure how to solve for the basis at this point.

I'm also unsure if what I did for rref was correct because vectors are usually denoted by column spaces, rather than what row spaces such as what I have done.

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