Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v (13,54); B = {(1,0), (0, 1)} for R². = (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v (13,54); B = {(1,0), (0, 1)} for R². = (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
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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![Either find the coordinates of the vector relative to basis B,
or find the original vector from the coordinates relative to basis B.
(a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³.
(b) v = (13,54); B = {(1,0), (0, 1)} for R².
(c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39ee3059-6733-456c-bbc4-46bedd3c18f2%2Fc9f72e71-fbe3-43bd-b17a-6d4624a57993%2Fnx7y75q_processed.png&w=3840&q=75)
Transcribed Image Text:Either find the coordinates of the vector relative to basis B,
or find the original vector from the coordinates relative to basis B.
(a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³.
(b) v = (13,54); B = {(1,0), (0, 1)} for R².
(c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
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