AnswerNote first that the vectors 71, 72, and 73 are linearly independent (a necessary precondition for performingthe Gram-Schmidt process); you can check this by row-reducing the coefficient matrix [₁confirming that all three columns have pivots. Gram-Schmidt then produces the orthogonal basis2 3] and1/2-2/3{V1, U2, U3} =2/31812/30If you like, you can scale the second and third vectors to clear fractions (the result will still be an orthogonalbasis). Consider the vectors€₁ =₂ =3: = 1in R4. Use the Gram-Schmidt process to find an orthogonal basis for the subspace span{1, 72, 73}.

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Answered: Consider the vectors 7₁ = €₂ = T3 = 1…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...

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Consider the vectors 7₁ = €₂ = T3 = 1 in R4. Use the Gram-Schmidt process to find an orthogonal basis for the subspace span{1, 72, 73}.