Let b₁ = [13] and b2 [3] 5 a basis for R2. Let T : R² → R² be a linear transformation such that T(6₁) = 561 + 662 and T(62) = 261 +562. (a) The matrix of T relative to the basis B is MBB(T) [TB = The set B = MEE(T) = [T]E (b) The matrix of T relative to the standard basis E for R² is - {6₁, 6₂} is [00]
Let b₁ = [13] and b2 [3] 5 a basis for R2. Let T : R² → R² be a linear transformation such that T(6₁) = 561 + 662 and T(62) = 261 +562. (a) The matrix of T relative to the basis B is MBB(T) [TB = The set B = MEE(T) = [T]E (b) The matrix of T relative to the standard basis E for R² is - {6₁, 6₂} is [00]
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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Question
![2
Let b₁ = [¹3]
61
- [3³]
-3
5
a basis for R2. Let T : R² → R2 be a linear transformation
such that T(6₁) = 561 + 6b2 and T(62) = 26₁ +5b2.
and b2
(a) The matrix of T relative to the basis B is
MBB(T) [T] B =
The set B =
Mee(T) = [T]e
2
(b) The matrix of T relative to the standard basis E for R²
is
{6₁, 62} is
8
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Transcribed Image Text:2
Let b₁ = [¹3]
61
- [3³]
-3
5
a basis for R2. Let T : R² → R2 be a linear transformation
such that T(6₁) = 561 + 6b2 and T(62) = 26₁ +5b2.
and b2
(a) The matrix of T relative to the basis B is
MBB(T) [T] B =
The set B =
Mee(T) = [T]e
2
(b) The matrix of T relative to the standard basis E for R²
is
{6₁, 62} is
8
[00]
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