1.- Let T be a linear transformation such that: T: R² - [1,1] - [1,-1) - [1,1] [1,-1] R² 1-1,01 [2,1]. 1. Find the canonical matrix of T: M(T)E.E. 2. There is a basis B = (W₁, W₂) such that the vectors [1,1]" y [1,-1]" can be written as: W2 W₁ + W2. = 2W₁ - Find the matrix of T with respect to the canonical basis B: M(T)B,B-

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1.- Let T be a linear transformation such that:
T: R² -
[1,1] -
[1,-1)
-
[1,1]
[1,-1]
R²
1-1,01
[2,1].
1. Find the canonical matrix of T: M(T)E.E.
2. There is a basis B = (W₁, W₂) such that the vectors [1,1]" y [1,-1]" can be written as:
W2
W₁ + W2.
= 2W₁
-
Find the matrix of T with respect to the canonical basis B: M(T)B,B-
Transcribed Image Text:1.- Let T be a linear transformation such that: T: R² - [1,1] - [1,-1) - [1,1] [1,-1] R² 1-1,01 [2,1]. 1. Find the canonical matrix of T: M(T)E.E. 2. There is a basis B = (W₁, W₂) such that the vectors [1,1]" y [1,-1]" can be written as: W2 W₁ + W2. = 2W₁ - Find the matrix of T with respect to the canonical basis B: M(T)B,B-
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