transform the basis vectors into an orthonormal basis.

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Let 3 have the Euclidean inner product. Use Gram-Schmidt process to transform the basis vectors 1=(1,0,0),2=(3,7,−2),3=(0,4,1) into an orthonormal basis

I was able to find alpha1=(1/√2,0,0) but got lost after that can someone please help me out I have attached the picture of the solution where i think i am making a mistake

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