Find a linear transformation T: R² R³ such that (4) 0-1 0-1-0-H = and T T T = Try find a linear combination Hint: Leverage the original definition of a linear transformation, namely that T(u + v) = T(u) +T(v) for all vectors u, v and for all r ER = T(ru) = rT(u) which equals 3 }] B 8 and " H., and/or }] (H) 3 (B). Once you have these last two vectors, you can use the formula for the matrix of a linear map to find the desired matrix. use that linear combination to find T 2 and T then
Find a linear transformation T: R² R³ such that (4) 0-1 0-1-0-H = and T T T = Try find a linear combination Hint: Leverage the original definition of a linear transformation, namely that T(u + v) = T(u) +T(v) for all vectors u, v and for all r ER = T(ru) = rT(u) which equals 3 }] B 8 and " H., and/or }] (H) 3 (B). Once you have these last two vectors, you can use the formula for the matrix of a linear map to find the desired matrix. use that linear combination to find T 2 and T then
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Find a linear transformation T : R² → R³ such that
T
¹(H)-B₁ ¹(C)-1]. -(C)-1]
and T
= 2
=
=
T
Hint: Leverage the original definition of a linear transformation, namely that
T(u + v) = T(u) +T(v) for all vectors u, v
and for all r ER
T(ru) = rT(u)
H.Q
Try find a linear combination
[3]
[!] and [?]
8₁
(18]) and 2 (191)
T
Once you have these
last two vectors, you can use the formula for the matrix of a linear map to find the
desired matrix.
use that linear combination to find T
9
2
and/or
which equals
then](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cbca931-dab8-488b-9a97-d6989fbfb0ca%2F63bfd9e4-d7e5-45fd-938f-f78d0a100d09%2Fn3rdlzq_processed.png&w=3840&q=75)
Transcribed Image Text:Find a linear transformation T : R² → R³ such that
T
¹(H)-B₁ ¹(C)-1]. -(C)-1]
and T
= 2
=
=
T
Hint: Leverage the original definition of a linear transformation, namely that
T(u + v) = T(u) +T(v) for all vectors u, v
and for all r ER
T(ru) = rT(u)
H.Q
Try find a linear combination
[3]
[!] and [?]
8₁
(18]) and 2 (191)
T
Once you have these
last two vectors, you can use the formula for the matrix of a linear map to find the
desired matrix.
use that linear combination to find T
9
2
and/or
which equals
then
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