Show that the function is a linear transformation. Upload your proofs below. 1([33] 39 T(M) = M from R2x2 to R²×2 It is not a linear transformation. It is a linear transformation. Choose File No file chosen 2 Hint: To show that a map of T: R²×² → R²×² is a linear transformation you must show that T(M₁ + kM₂) = T(M₁) + kT(M₂) for all M₁, M₂ € R²×2 So start by taking arbitrary M₁, M₂ € R²×² and k € R ('arbitrary' means NOT examples) and com the righthand side: T(M₁) + KT (M₂) What can you factor out? Can you make this equal = M₁ 1¹1² [3 3] + (KM₂) [3 3] 1 3 T(M₁ + kM₂) = (M₁ + kM₂) | ? 39 ute
Show that the function is a linear transformation. Upload your proofs below. 1([33] 39 T(M) = M from R2x2 to R²×2 It is not a linear transformation. It is a linear transformation. Choose File No file chosen 2 Hint: To show that a map of T: R²×² → R²×² is a linear transformation you must show that T(M₁ + kM₂) = T(M₁) + kT(M₂) for all M₁, M₂ € R²×2 So start by taking arbitrary M₁, M₂ € R²×² and k € R ('arbitrary' means NOT examples) and com the righthand side: T(M₁) + KT (M₂) What can you factor out? Can you make this equal = M₁ 1¹1² [3 3] + (KM₂) [3 3] 1 3 T(M₁ + kM₂) = (M₁ + kM₂) | ? 39 ute
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
![Show that the function is a linear transformation. Upload your proofs below.
1
39
T(M)
= M
from R2×2 to R²×2
2x2
It is not a linear transformation.
It is a linear transformation.
Choose File No file chosen
→ R²X2
is a linear transformation you must show that
T(M₁ + kM₂) = T(M₁) + kT(M₂) for all M₁, M₂ € R² × ²
So start by taking arbitrary M₁, M₂ € R²×² and k € R ('arbitrary' means NOT examples) and compute
the righthand side:
Hint: To show that a map of T: R²×²
T(M₁) + kT(M₂)
What can you factor out? Can you make this equal
=
1
[33]
M₁
+ (kM₂)
T(M₁ + kM₂) = (M₁ + kM₂)
1 3
3
3]
1
[33] ²
39](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5468827-6e1c-400d-bb68-9da85e35a3db%2F1377a7f3-5964-457f-af0c-877358258313%2Fmb0e8f_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the function is a linear transformation. Upload your proofs below.
1
39
T(M)
= M
from R2×2 to R²×2
2x2
It is not a linear transformation.
It is a linear transformation.
Choose File No file chosen
→ R²X2
is a linear transformation you must show that
T(M₁ + kM₂) = T(M₁) + kT(M₂) for all M₁, M₂ € R² × ²
So start by taking arbitrary M₁, M₂ € R²×² and k € R ('arbitrary' means NOT examples) and compute
the righthand side:
Hint: To show that a map of T: R²×²
T(M₁) + kT(M₂)
What can you factor out? Can you make this equal
=
1
[33]
M₁
+ (kM₂)
T(M₁ + kM₂) = (M₁ + kM₂)
1 3
3
3]
1
[33] ²
39
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