A= = X = [1 #1 X2 X3 X4 -4x2+1 ₁+ 4 13+0 x₂ +0x3+4 ₁ + 0x₂+-4 X3 Then AX = 0 the span of {M₁, M₂}, where 1 0 XA if and only if #₁, 2, 3, 4 satisfies the following system of linear equations: *4 = 0 e set of 2 x 2 matrices X satisfying *4 = 0 4x4 = 0 AX = XA
A= = X = [1 #1 X2 X3 X4 -4x2+1 ₁+ 4 13+0 x₂ +0x3+4 ₁ + 0x₂+-4 X3 Then AX = 0 the span of {M₁, M₂}, where 1 0 XA if and only if #₁, 2, 3, 4 satisfies the following system of linear equations: *4 = 0 e set of 2 x 2 matrices X satisfying *4 = 0 4x4 = 0 AX = XA
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
![Let A =
Let X =
021
1
[81]
4
x₁
| X3
4x2+
-12₁+4
1
10
M₂ =
0
1
X2
X4
3+0
₂+0x3+ 4
₁ + 0x₂+ -4 X3
Then AX = XA if and only if x₁, T2, T3, T4 satisfies the following system of linear equations:
is the span of {M₁, M₂}, where
M₁ =
0
1
The set of 2 x 2 matrices X satisfying
*4 = 0
x₁ = 0
4x4 0
AX = XA](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefe71c64-8346-40ed-b3ed-a6b5092127b6%2F32e54736-ee72-41f5-bc52-3a1b3be76002%2F9n1lzjr_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
Let X =
021
1
[81]
4
x₁
| X3
4x2+
-12₁+4
1
10
M₂ =
0
1
X2
X4
3+0
₂+0x3+ 4
₁ + 0x₂+ -4 X3
Then AX = XA if and only if x₁, T2, T3, T4 satisfies the following system of linear equations:
is the span of {M₁, M₂}, where
M₁ =
0
1
The set of 2 x 2 matrices X satisfying
*4 = 0
x₁ = 0
4x4 0
AX = XA
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