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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
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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