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GRAM-SCHMIDT | SAMPLE ITEM Perhaps the ordered B = {(1, -1, 0), (-1, 0, 1), (0, 1, -1)}. a) Use the Gram-Schmidt process to convert B to an orthonormal basis B* for R³ with respect to the standard inner product. b) Let v = (1, -4, 3). Find the coordinates of v relative to the orthonormal basis B* obtained in letter (a).

GRAM-SCHMIDT | SAMPLE ITEM Perhaps the ordered B = {(1, -1, 0), (-1, 0, 1), (0, 1, -1)}. a) Use the Gram-Schmidt process to convert B to an orthonormal basis B* for R³ with respect to the standard inner product. b) Let v = (1, -4, 3). Find the coordinates of v relative to the orthonormal basis B* obtained in letter (a).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 16CM
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GRAM-SCHMIDT | SAMPLE ITEM Perhaps the ordered B = {(1, -1, 0), (-1, 0, 1), (0, 1, -1)}. a) Use the Gram-Schmidt process to convert B to an orthonormal basis B* for R³ with respect to the standard inner product. b) Let v = (1, -4, 3). Find the coordinates of v relative to the orthonormal basis B* obtained in letter (a).
Transcribed Image Text:GRAM-SCHMIDT | SAMPLE ITEM Perhaps the ordered B = {(1, -1, 0), (-1, 0, 1), (0, 1, -1)}. a) Use the Gram-Schmidt process to convert B to an orthonormal basis B* for R³ with respect to the standard inner product. b) Let v = (1, -4, 3). Find the coordinates of v relative to the orthonormal basis B* obtained in letter (a).
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