1. Let U = span 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. (b) Let x = H 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. ii. Using your answer in (b), compute Tu(x), the orthogonal pro- jection of x onto the subspace U.

1. Let U = span 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. (b) Let x = H 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. ii. Using your answer in (b), compute Tu(x), the orthogonal pro- jection of x onto the subspace U.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 49E

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