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I'm confused by the term homogenous in linear algebra. Being homogenous means to have the matrix = 0 and if its homogenous, it can either have infinite solutions or a unique. No solutions is impossible but how? 1 O 0 = 1= Here we're basically saying 1 = 0 which isn't true. which would mean it's inconsistent which would mean no solution. Can someone explain please? Do we imagine theres an x infront of the 1 which would make it x=0 which could be true? If the table looked like the below id understand because this is non homogenous system and non homogenous systems can have no solution as O does not equal 1. 00=1 00=1 O O

I'm confused by the term homogenous in linear algebra. Being homogenous means to have the matrix = 0 and if its homogenous, it can either have infinite solutions or a unique. No solutions is impossible but how? 1 O 0 = 1= Here we're basically saying 1 = 0 which isn't true. which would mean it's inconsistent which would mean no solution. Can someone explain please? Do we imagine theres an x infront of the 1 which would make it x=0 which could be true? If the table looked like the below id understand because this is non homogenous system and non homogenous systems can have no solution as O does not equal 1. 00=1 00=1 O O

Advanced Engineering Mathematics
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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I'm confused by the term homogenous in linear algebra. Being homogenous means to have the matrix = 0 and if its homogenous, it can either have infinite solutions or a unique. No solutions is impossible but how? 1 O 0 = 1= Here we're basically saying 1 = 0 which isn't true. which would mean it's inconsistent which would mean no solution. Can someone explain please? Do we imagine theres an x infront of the 1 which would make it x=0 which could be true? 00=1 00=1 If the table looked like the below id understand because this is non homogenous system and non homogenous systems can have no solution as 0 does not equal 1. O O
Transcribed Image Text:I'm confused by the term homogenous in linear algebra. Being homogenous means to have the matrix = 0 and if its homogenous, it can either have infinite solutions or a unique. No solutions is impossible but how? 1 O 0 = 1= Here we're basically saying 1 = 0 which isn't true. which would mean it's inconsistent which would mean no solution. Can someone explain please? Do we imagine theres an x infront of the 1 which would make it x=0 which could be true? 00=1 00=1 If the table looked like the below id understand because this is non homogenous system and non homogenous systems can have no solution as 0 does not equal 1. O O
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