## Linear Algebra: Orthonormal Basis

1. The problem statement, all variables and given/known data

Find an orthonormal basis for the subspace of R^4 that is spanned by the vectors: (1,0,1,0), (1,1,1,0), (1,-1,0,1), (3,4,4,-1)

3. The attempt at a solution

When I try to use the Gram-Schmidt process, I am getting (before normalization): (1,0,1,0), (0,1,0,0), (1,0,-1,2), (0,0,0,0). So obviously there is some mistake that I am making but I have checked this at least 3 times. Can someone help me and let me know if it is something on my end or the problem. Thank you.
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 Recognitions: Homework Help Science Advisor Without have actually worked it out fully, why do you think you made a mistake? The dimension of the subspace is less than 4. You are only going to get a number of orthonormal vectors equal to the dimension of the subspace.

 Quote by Dick Without have actually worked it out fully, why do you think you made a mistake? The dimension of the subspace is less than 4. You are only going to get a number of orthonormal vectors equal to the dimension of the subspace.
I thought that the basis had to span R^4? And since of of the elements was (0,0,0,0) the basis can't span R^4.

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## Linear Algebra: Orthonormal Basis

 Quote by tylerc1991 I thought that the basis had to span R^4? And since of of the elements was (0,0,0,0) the basis can't span R^4.
It doesn't span R^4. It spans the subspace of R^4 spanned by the given vectors.

 Quote by Dick It doesn't span R^4. It spans the subspace of R^4 spanned by the given vectors.
I see. So will (0,0,0,0) be included in the orthonormal basis?

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