Let B = {v1, V2, V3} be a basis for R3. For any u, v E R³ define||(u, v) = [u]E[v]B.•(a) Is (,) an inner product?(b) Can you find a matrix A (constructed using v1, V2, and v3) such that(u, v) = u" Av?

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Let B = {v1, v2, v3} be a basis for R3. For any u, v E R³ define (u, v) = [u]%[v]B• (a) Is (,) an inner product?

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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Let B = {v1, V2, V3} be a basis for R3. For any u, v E R³ define
||
(u, v) = [u]E[v]B.
•
(a) Is (,) an inner product?
(b) Can you find a matrix A (constructed using v1, V2, and v3) such that
(u, v) = u" Av?

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