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1. Let T: R3 R3 be a linear image, which satisfies that (-3 Tei = -3/22, T(ez) = 9/2 and T (es) = -3 2 where E = {ei, ez, eg) is the standard base in R3.

1. Let T: R3 R3 be a linear image, which satisfies that (-3 Tei = -3/22, T(ez) = 9/2 and T (es) = -3 2 where E = {ei, ez, eg) is the standard base in R3.

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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I. Let T: R3 R3 be a linear image, which satisfies that -3 2 Tei = -3/2,T(ez) = 9/2 and T (es) = 2 where E = {ei, ez, eg) is the standard base in R3. (A) Determine the image of y V= 1 under the image T. (b) Determine all the vectors in R3 that T maps to the zero vector. (<) Decide on the vector IN belongs to the image of T.
Transcribed Image Text:I. Let T: R3 R3 be a linear image, which satisfies that -3 2 Tei = -3/2,T(ez) = 9/2 and T (es) = 2 where E = {ei, ez, eg) is the standard base in R3. (A) Determine the image of y V= 1 under the image T. (b) Determine all the vectors in R3 that T maps to the zero vector. (<) Decide on the vector IN belongs to the image of T.
1. Låt T : R3 → R³ vara en linjär avbilding som uppfyller att (+) 1 -3 2 T(e1) = -3/2 T(e2) = | 9/2 och T(e3) = -3 4 där E = {e1, e2, e3} är standardbasen i R3. (a) Bestäm bilden av () v = under avbildningen T. (b) Bestäm alla vektorer i R³ som T avbildar på nollvektorn. (c) Avgör om vektorn 4 w = -6 -8 tillhör bilden av T. 5
Transcribed Image Text:1. Låt T : R3 → R³ vara en linjär avbilding som uppfyller att (+) 1 -3 2 T(e1) = -3/2 T(e2) = | 9/2 och T(e3) = -3 4 där E = {e1, e2, e3} är standardbasen i R3. (a) Bestäm bilden av () v = under avbildningen T. (b) Bestäm alla vektorer i R³ som T avbildar på nollvektorn. (c) Avgör om vektorn 4 w = -6 -8 tillhör bilden av T. 5
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