Let A = [69]. W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X M₂x2 (C): AX = iX} 1 [] and B It is given that are subspaces of M₂x2 (C). (1.1) Find a basis for W₁. (1.2) Find a basis for W₁n W₂. (1.3) Explain whether M₂x2 (C) = W₁ W₂.
Let A = [69]. W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X M₂x2 (C): AX = iX} 1 [] and B It is given that are subspaces of M₂x2 (C). (1.1) Find a basis for W₁. (1.2) Find a basis for W₁n W₂. (1.3) Explain whether M₂x2 (C) = W₁ W₂.
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
B2.
![QUESTION 1
· [
Let A =
0 1
-1 0
:]
W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X € M₂x2 (C): AX = ix}
and B =
[
º;].
i 0
0 -i
It is given that
are subspaces of M₂x2 (C).
(1.1) Find a basis for W₁.
(1.2) Find a basis for W₁n W₂.
(1.3) Explain whether M₂x2 (C) = W₁ W₂.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F614d5e2e-8a04-4ef9-a31d-d2f8fb345e7f%2Fa2affc90-fd3e-427b-9086-3bf3bab7457f%2Fjrobd3_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 1
· [
Let A =
0 1
-1 0
:]
W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X € M₂x2 (C): AX = ix}
and B =
[
º;].
i 0
0 -i
It is given that
are subspaces of M₂x2 (C).
(1.1) Find a basis for W₁.
(1.2) Find a basis for W₁n W₂.
(1.3) Explain whether M₂x2 (C) = W₁ W₂.
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