Consider the functions T₁ : M₂2 → R² and T₂ : R² → M22 satisfying T₁ ([a b]) = (a, d), T₂(1,0) = [!!] 00 (a) Show that T₁ is a linear transformation. (b) The function T₂ is a linear transformation. Find T₂(a, b). (c) Are T₁ T₂ and T₂ o T₁ linear? / 17) T₂(0, 1) = [ii]
Consider the functions T₁ : M₂2 → R² and T₂ : R² → M22 satisfying T₁ ([a b]) = (a, d), T₂(1,0) = [!!] 00 (a) Show that T₁ is a linear transformation. (b) The function T₂ is a linear transformation. Find T₂(a, b). (c) Are T₁ T₂ and T₂ o T₁ linear? / 17) T₂(0, 1) = [ii]
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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![9. Consider the functions T₁ : M22 → R² and T₂ : R² → M22 satisfying
( [o
d]) = (a, d),
T₁
T₂(1,0) = []
(a) Show that T₁ is a linear transformation.
(b) The function T₂ is a linear transformation. Find T₂(a, b).
(c) Are T₁ T₂ and T₂ o T₁ linear?
(d) Find T₁ T₂(a, b) and T₂0 T₁
O
([d]).
"
T₂(0, 1) =
=
[1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2F70d55cf8-96a4-42e6-afd4-e509ecf1436b%2F0tduf3f_processed.png&w=3840&q=75)
Transcribed Image Text:9. Consider the functions T₁ : M22 → R² and T₂ : R² → M22 satisfying
( [o
d]) = (a, d),
T₁
T₂(1,0) = []
(a) Show that T₁ is a linear transformation.
(b) The function T₂ is a linear transformation. Find T₂(a, b).
(c) Are T₁ T₂ and T₂ o T₁ linear?
(d) Find T₁ T₂(a, b) and T₂0 T₁
O
([d]).
"
T₂(0, 1) =
=
[1
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