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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(c) Using the Gram-Schmidt orthogonalization, turn the basis of U you got in (a) into an orthogonal basis.
Transcribed Image Text:(c) Using the Gram-Schmidt orthogonalization, turn the basis of U you got in (a) into an orthogonal basis.
1. Let U = span (4) 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 = 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.
Transcribed Image Text:1. Let U = span (4) 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 = 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.
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