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
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...
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