Let B = {(0, 2, −2), (1, 0, −2)} be a basis for a subspace of R3, and consider x = (−1, 4, −2), a vector in the subspace.(a) Write x as a linear combination of the vectors in B. That is, find the coordinates of x relative to B.(b) Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B′.(c) Write x as a linear combination of the vectors in B′. That is, find the coordinates of x relative to B′.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let B = {(0, 2, −2), (1, 0, −2)} be a basis for a subspace of R3, and consider x = (−1, 4, −2), a vector in the subspace.
(a) Write x as a linear combination of the vectors in B. That is, find the coordinates of x relative to B.
(b) Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B′.
(c) Write x as a linear combination of the vectors in B′. That is, find the coordinates of x relative to B′.

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