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how do I find the basis for all vectors that are perpendicular to both

v1 = (1,1,0,0) and

v2 = (1,0,1,1)

If it were 3-D I could find a normal vector via cross product, but in n-dimensions.... what do I do?

My one thought is to arrange and solve linear homogeneous system:

[v1][x] = 0

[v2][y] = 0

since RHS is the dot product of the row vector (v1 or v2) and the column [x,y]^{t}, and for vectors to be perpendicular, their dot product should be 0.

Is that correct?

Thanks in advance.

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# Perpendicular vector

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