This question concerns the linear transformation t from Question 3, given by t: R³ R³ (x, y, z) (2x, y + z, z-x), and also the linear transformation s given by S: R³ → P3 (a, b, c)→a-b+ (b+c)x+ (a + c)x². (a) Write down the matrix of s, and find the matrix of sot, in both cases with respect to the standard bases for R³ and P3. (b) Find Kers, and describe it geometrically.
This question concerns the linear transformation t from Question 3, given by t: R³ R³ (x, y, z) (2x, y + z, z-x), and also the linear transformation s given by S: R³ → P3 (a, b, c)→a-b+ (b+c)x+ (a + c)x². (a) Write down the matrix of s, and find the matrix of sot, in both cases with respect to the standard bases for R³ and P3. (b) Find Kers, and describe it geometrically.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...
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![This question concerns the linear transformation t from Question 3, given by
t: R³
R³
(x, y, z)
(2x, y + z, z-x),
and also the linear transformation s given by
S: R³ → P3
(a, b, c)→a-b+ (b+c)x+ (a + c)x².
(a) Write down the matrix of s, and find the matrix of sot, in both cases
with respect to the standard bases for R³ and P3.
(b) Find Kers, and describe it geometrically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4f3c4ec-fe5b-4d14-92c7-f03ecdbdce74%2F803f803a-a02d-4135-afe6-1c32fb51e4d8%2Fgrph4jb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This question concerns the linear transformation t from Question 3, given by
t: R³
R³
(x, y, z)
(2x, y + z, z-x),
and also the linear transformation s given by
S: R³ → P3
(a, b, c)→a-b+ (b+c)x+ (a + c)x².
(a) Write down the matrix of s, and find the matrix of sot, in both cases
with respect to the standard bases for R³ and P3.
(b) Find Kers, and describe it geometrically.
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