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Okay I have a set of vectors {(-2, 3, 1, 0), (3, 0, -1, 2)} and I need to create a basis in R4. How do I do that? These vectors and lineary independent but I need two more vectors for the basis.

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1 Answer

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If you just want four linearly independent vectors in the end (you don't care about orthogonality and such), then picking from the standard basis vectors also works. For instance, it is pretty clear that $(0,1,0,0)$ is linearly independent from the two vectors that you have. Now you just have to check the other three (odds are any of them would work, but you will have to check to be certain).

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