1. Given: 1. Vector i= (1,1,1) (in standard basis) 2. The linear transform (in standard basis) T: R→R' where T is defined as (x+ y+z, 2x - y-2z,3x- y- z). [1 0 1] 3. The new basis P=1 -1 0 which spans R 2 1 b) What is the result when T acts on vector ? d) Use the change of basis matrix to write the result in b) in terms of the new basis, P. e) Obtain the same result, but this time by first writing the transform itself in terms of the new basis. Remember that P'AP represents the transform, T with respect to the new basis, P.
1. Given: 1. Vector i= (1,1,1) (in standard basis) 2. The linear transform (in standard basis) T: R→R' where T is defined as (x+ y+z, 2x - y-2z,3x- y- z). [1 0 1] 3. The new basis P=1 -1 0 which spans R 2 1 b) What is the result when T acts on vector ? d) Use the change of basis matrix to write the result in b) in terms of the new basis, P. e) Obtain the same result, but this time by first writing the transform itself in terms of the new basis. Remember that P'AP represents the transform, T with respect to the new basis, P.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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![1. Vector i = (1,1,1) (in standard basis)
2. The linear transform (in standard basis) T: R R' where Tis defined as
(x+ y+ z, 2x - y- 2z,3x - y- z).
1. Given:
[1 0 1]
3. The new basis P=1 -1 0 which spans R
2
1
b) What is the result when T acts on vector i?
d) Use the change of basis matrix to write the result in b) in terms of the new basis, P.
e) Obtain the same result, but this time by first writing the transform itself in terms of the new basis. Remember that
P'AP represents the transform, T with respect to the new basis, P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cd5d89c-4a08-4e09-9294-d87ceb85eb16%2F1aa537cb-6a6c-4e94-8979-8e42a4ed2422%2Fllrmxe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Vector i = (1,1,1) (in standard basis)
2. The linear transform (in standard basis) T: R R' where Tis defined as
(x+ y+ z, 2x - y- 2z,3x - y- z).
1. Given:
[1 0 1]
3. The new basis P=1 -1 0 which spans R
2
1
b) What is the result when T acts on vector i?
d) Use the change of basis matrix to write the result in b) in terms of the new basis, P.
e) Obtain the same result, but this time by first writing the transform itself in terms of the new basis. Remember that
P'AP represents the transform, T with respect to the new basis, P.
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