7. Consider the ordered bases S and T of R: ()} S = {81, 82, $3} and T = {t1, t2, t3} = We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3. (a) Find the matrix Pr-s = [Id]} of the basis change from S to T. (b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map. (c) Find the matrix [L] of L using the ordered basis T for the domain and range of the map.
7. Consider the ordered bases S and T of R: ()} S = {81, 82, $3} and T = {t1, t2, t3} = We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3. (a) Find the matrix Pr-s = [Id]} of the basis change from S to T. (b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map. (c) Find the matrix [L] of L using the ordered basis T for the domain and range of the map.
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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![7. Consider the ordered bases S and T of R:
()}
S = {81, 82, $3}
and T = {t1, t2, t3} =
We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3.
(a) Find the matrix Pr-s = [Id]} of the basis change from S to T.
(b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map.
(c) Find the matrix [L] of L using the ordered basis T for the domain and
range
of the
map.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cac1a6-5ad9-4f72-bdd9-21a202e53df4%2Fbad7d01a-9098-40a2-90d0-a36770f11eee%2Fz61ajr.png&w=3840&q=75)
Transcribed Image Text:7. Consider the ordered bases S and T of R:
()}
S = {81, 82, $3}
and T = {t1, t2, t3} =
We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3.
(a) Find the matrix Pr-s = [Id]} of the basis change from S to T.
(b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map.
(c) Find the matrix [L] of L using the ordered basis T for the domain and
range
of the
map.
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