Let TV V be a linear map. Consider two distinct bases of V: B = 1, V2, V3) and C = (v₁, v2 + v3, v2 — v3). Determine the matrix of change of bases P such that [T]c = P−¹ × [T]ß × P. /1 0 0 1 O O O P || = P = P P = IL 0 0 1 1 1 -1 0 1 0 0 1 -1 0 1 1 00 - 1212 HIN 0 0
Let TV V be a linear map. Consider two distinct bases of V: B = 1, V2, V3) and C = (v₁, v2 + v3, v2 — v3). Determine the matrix of change of bases P such that [T]c = P−¹ × [T]ß × P. /1 0 0 1 O O O P || = P = P P = IL 0 0 1 1 1 -1 0 1 0 0 1 -1 0 1 1 00 - 1212 HIN 0 0
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 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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![Let TV→ V be a linear map. Consider two distinct bases of V: B =
(v₁,
v1, v2,v3) and
C = (v₁, v2 + v3, v2 — v3). Determine the matrix of change of bases P such that
[T]c = P¹ × [T] B × P.
/1 0 0
0 1 1
0
1 -1
O
O
O
P
||
=
P =
P
P =
||
1
1|21|2
1
0
0
1 -1
0 1 1
O 1|21|2
OTHIN
0
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b60fa95-9b4b-4fa6-a572-04dc2e43c26e%2F3029e5e5-fd4f-4ff9-96c1-1db4b7890391%2F6iyz34_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let TV→ V be a linear map. Consider two distinct bases of V: B =
(v₁,
v1, v2,v3) and
C = (v₁, v2 + v3, v2 — v3). Determine the matrix of change of bases P such that
[T]c = P¹ × [T] B × P.
/1 0 0
0 1 1
0
1 -1
O
O
O
P
||
=
P =
P
P =
||
1
1|21|2
1
0
0
1 -1
0 1 1
O 1|21|2
OTHIN
0
0
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