Problem 1. Let B be the basis of F3 given by the list V₁, V2, U3, where -0. --D]. V₂ A V₁ = V3 1.1. Find a formula for coordinate vector [v], where v=b €³. - 8 С 1.2. Since B is a basis, there is a linear transformation T: F3 → M₂(F) with T(v₁) = (1 7¹). T(v₂2) = (1-1), - (1 9), T(vs) = (-¹1 9). Find a formula for T(v), where v is as in Problem 1.1. 1.3. Now let 6 be the basis E11, E12, E21, E22 of M₂(F), and let S = TOTEL(F³, F¹), where T is as in Problem 1.2 and Te: M₂(F) → F¹ is the coordinate transfor- mation of M₂ (F) with respect to 6. Find a general formula for S(v), where v is as in Problem 1.1.
Problem 1. Let B be the basis of F3 given by the list V₁, V2, U3, where -0. --D]. V₂ A V₁ = V3 1.1. Find a formula for coordinate vector [v], where v=b €³. - 8 С 1.2. Since B is a basis, there is a linear transformation T: F3 → M₂(F) with T(v₁) = (1 7¹). T(v₂2) = (1-1), - (1 9), T(vs) = (-¹1 9). Find a formula for T(v), where v is as in Problem 1.1. 1.3. Now let 6 be the basis E11, E12, E21, E22 of M₂(F), and let S = TOTEL(F³, F¹), where T is as in Problem 1.2 and Te: M₂(F) → F¹ is the coordinate transfor- mation of M₂ (F) with respect to 6. Find a general formula for S(v), where v is as in Problem 1.1.
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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![Problem 1. Let be the basis of F3 given by the list v₁, V2, V3, where
A
V₁ =
H
7
v₂ =
D
V3 =
1.1. Find a formula for coordinate vector [v], where
a
v=b € F³.
[G]
с
1.2. Since B is a basis, there is a linear transformation T: F³ → M₂ (F) with
T(v₁) = (₁ 1¹), T(0₂) = (19), T(v₁) = (-¹1
(-19).
Find a formula for T(v), where v is as in Problem 1.1.
1.3. Now let be the basis E₁1, E12, E21, E22 of M₂(F), and let
S = TOTEL(F³, F¹),
where T is as in Problem 1.2 and Te : M₂(F) → F4 is the coordinate transfor-
mation of M₂ (F) with respect to C. Find a general formula for S(v), where
v is as in Problem 1.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18306282-f933-4068-a09a-779164b2089a%2F3b8c0388-8683-43eb-9ed5-841f6bb9313c%2Fwfx6kb_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. Let be the basis of F3 given by the list v₁, V2, V3, where
A
V₁ =
H
7
v₂ =
D
V3 =
1.1. Find a formula for coordinate vector [v], where
a
v=b € F³.
[G]
с
1.2. Since B is a basis, there is a linear transformation T: F³ → M₂ (F) with
T(v₁) = (₁ 1¹), T(0₂) = (19), T(v₁) = (-¹1
(-19).
Find a formula for T(v), where v is as in Problem 1.1.
1.3. Now let be the basis E₁1, E12, E21, E22 of M₂(F), and let
S = TOTEL(F³, F¹),
where T is as in Problem 1.2 and Te : M₂(F) → F4 is the coordinate transfor-
mation of M₂ (F) with respect to C. Find a general formula for S(v), where
v is as in Problem 1.1.
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