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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). Given [1 0 -1] 3. The new basis P = 3 4 -2 which spans R' 3 5 -2 Write vector in terms of the new basis, P. Write the linear transformation of i according to the new basis, P, by transforming it first, then writing the result according to the new basis. Write the linear transformation of X according to the new basis, P, by writing it according to the new basis, and then transforming it also in the new basis.

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). Given [1 0 -1] 3. The new basis P = 3 4 -2 which spans R' 3 5 -2 Write vector in terms of the new basis, P. Write the linear transformation of i according to the new basis, P, by transforming it first, then writing the result according to the new basis. Write the linear transformation of X according to the new basis, P, by writing it according to the new basis, and then transforming it also in the new basis.

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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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+22). 2. Given [1 0 -1 3. The new basis P =|3 4 - 2 which spans R 3 5 -2 d) Write vector i in terms of the new basis, P. e) Write the lincar transformation of i according to the new basis, P, by transforming it first, then writing the result according to the new basis. ) 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: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+22). 2. Given [1 0 -1 3. The new basis P =|3 4 - 2 which spans R 3 5 -2 d) Write vector i in terms of the new basis, P. e) Write the lincar transformation of i according to the new basis, P, by transforming it first, then writing the result according to the new basis. ) 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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