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(Solved): 8. Use the Gram-Schmidt process to find an orthonormal basis for the subspace of \( \mathbb{R}^{4} ...
8. Use the Gram-Schmidt process to find an orthonormal basis for the subspace of \( \mathbb{R}^{4} \) spanned by \( \mathbf{x}_{1}=(4,2,2,1)^{T}, \mathbf{x}_{2}=(2,0,0,2)^{T} \), and \( \mathbf{x}_{3}=(1,1,-1,1)^{T} \)
Expert Answer
u1= x1 = (4,2,2,1) u2 = x2?x2.u1u1.u1u1 here x2.u1= 8+2 =10 u1.u1 = 16+4+4+1=25 So u2= (2,0,0,2)- ?25(4,2,2,1)=(25,?45,?45,85) so