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I have two homogeneous systems S1 and S2. The solution for

NS(S1) = {[-2,1,0], [-1,0,1]},

NS(S2) = {[-2,1,0], [-3,0,1]}.

I know that in a system if u and v are vectors, the sum of u+v is also a solution in the homogeneous system. i.e. S1=span{[-2,1,0], [-1,0,1]} then [-2,1,0] + [-1,0,1] is also a solution in that system (close under addition if I am correct).

But what about if I want to find the set of vectors which are solution to both S1 and S2? Do I use the same methods to it?

i.e. Solution = span {[-2,1,0]+[-2,1,0] ; [-1,0,1]+[-3,0,1]}

I think this is wrong, but I'm not sure how

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# Set of vector which are solution to 2 homogeneous systems

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