A homogeneous system of equations is a system of the form a12 ain ... a11 X2 aml Am2 Amn (b) Prove that a homogeneous system has a nontrivial solution if and only if the system has at least one free variable. DO ... O
A homogeneous system of equations is a system of the form a12 ain ... a11 X2 aml Am2 Amn (b) Prove that a homogeneous system has a nontrivial solution if and only if the system has at least one free variable. DO ... O
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
![A homogeneous system of equations is a system of the form
X1
a12
ain
x2
ат1
Am2
Amn
Xn
|0
(b) Prove that a homogeneous system has a nontrivial solution if and only if the system has
at least one free variable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0f3b9f2-9bd0-4a2f-a84e-f9430655910a%2F58377c55-40a3-46a6-8617-52a1f74ba2bc%2Fnlnns1_processed.png&w=3840&q=75)
Transcribed Image Text:A homogeneous system of equations is a system of the form
X1
a12
ain
x2
ат1
Am2
Amn
Xn
|0
(b) Prove that a homogeneous system has a nontrivial solution if and only if the system has
at least one free variable.
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