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1. Vector i = (1,-1,2) (in standard basis) 2. The linear transform (in standard basis) T: R'→R' where T is defined as (x – 3y, x- y- z, y + 2z). 1 0 3. The new basis P = 3 4 -2 which spans R' 3 5 -2

1. Vector i = (1,-1,2) (in standard basis) 2. The linear transform (in standard basis) T: R'→R' where T is defined as (x – 3y, x- y- z, y + 2z). 1 0 3. The new basis P = 3 4 -2 which spans R' 3 5 -2

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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2. Given 1. Vector i = (1,-1,2) (in standard basis) 2. The linear transform (in standard basis) T: R'→R where T is defined as (х- Зу, х — у — г, у + 2z). 1 0 -1 3. The new basis P =|3 4 - 2 which spans R 3 5 -2
Transcribed Image Text:2. Given 1. Vector i = (1,-1,2) (in standard basis) 2. The linear transform (in standard basis) T: R'→R where T is defined as (х- Зу, х — у — г, у + 2z). 1 0 -1 3. The new basis P =|3 4 - 2 which spans R 3 5 -2
d) Write vector x in terms of the new basis, P. e) Write the linear transformation of X according to the new basis, P, by transforming it first, then writing the result according to the new basis. f) Write the linear transformation of * according to the new basis, P, by writing it according to the new basis, and then transforming it also in the new basis.
Transcribed Image Text:d) Write vector x in terms of the new basis, P. e) Write the linear transformation of X according to the new basis, P, by transforming it first, then writing the result according to the new basis. f) Write the linear transformation of * according to the new basis, P, by writing it according to the new basis, and then transforming it also in the new basis.
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