QUESTION 1 Let A = 0 1 [9] and B-[9] 0 W₁ = {X € M₂x2 (C): AX = XB) and W₂ = {X € M₂x2 (C): AX = IX} It is given that are subspaces of M₂x2 (C). (1.1) Find a basis for W₁. (1.2) Find a basis for W₁ W₂. (1.3) Explain whether M2x2 (C) = W₁ W₂.
QUESTION 1 Let A = 0 1 [9] and B-[9] 0 W₁ = {X € M₂x2 (C): AX = XB) and W₂ = {X € M₂x2 (C): AX = IX} It is given that are subspaces of M₂x2 (C). (1.1) Find a basis for W₁. (1.2) Find a basis for W₁ 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
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![QUESTION 1
01
i
· [ 9₁ and B-[62]
3]
=
It is given that
-1 0
W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X M₂x2 (C): AX = IX}
Let A =
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%2Fabdd1821-d7b6-4171-a67e-edf70418727b%2F1ebd6552-cf78-4224-9d20-63c2e5d487a3%2F6fhpm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 1
01
i
· [ 9₁ and B-[62]
3]
=
It is given that
-1 0
W₁ = {X € M₂x2 (C): AX = XB} and W₂ = {X M₂x2 (C): AX = IX}
Let A =
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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