(c) Using the Gram-Schmidt orthogonalization, turn the basis of U yougot in (a) into an orthogonal basis. 1. Let U = span(4)be a subspace of R³. Answer the followingquestions based on this given U and the use of the dot product as theinner product:(a) Find a basis for U.(b) Let x =i. Using the basis you found in (a), create a matrix B and use thismatrix to find the coordinate vector, A, of x in terms of subspaceU.ii. Using your answer in (b), compute Tu(x), the orthogonal pro-jection of x onto the subspace U.

Answered: Image /qna-images/answer/d26fdc57-3f7c-4ce2-9fe6-f55177231475.jpg

1. Let U = span (80) be a subspace of R³. Answer the following questions based on this given U and the use of the dot product as the inner product: (a) Find a basis for U. i. Using the basis you found in (a), create a matrix B and use this matrix to find the coordinate vector, A, of x in terms of subspace U. (b) Let x = 0 H

1. Let U = span (80) be a subspace of R³. Answer the following questions based on this given U and the use of the dot product as the inner product: (a) Find a basis for U. i. Using the basis you found in (a), create a matrix B and use this matrix to find the coordinate vector, A, of x in terms of subspace U. (b) Let x = 0 H

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 45E

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