Solving a System by Gaussian Elimination: Help Needed

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SUMMARY

This discussion centers on solving a system of equations using Gaussian elimination to determine if the vector a=(10,11,4) belongs to the span of vectors v1=(2,1,4), v2=(-1,-2,1), and v3=(3,3,-1). The user initially struggles with the elimination process, particularly in achieving the necessary zeroes in the bottom row of the augmented matrix. Ultimately, the user resolves the issue after a fresh attempt, attributing the initial confusion to fatigue.

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  • Understanding of Gaussian elimination
  • Familiarity with vector spaces and spans
  • Basic linear algebra concepts
  • Ability to manipulate matrices
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  • Learn about vector spans and their significance in linear algebra
  • Practice solving systems of equations using different methods
  • Explore common pitfalls in matrix manipulation and how to avoid them
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Students of linear algebra, educators teaching Gaussian elimination, and anyone seeking to improve their problem-solving skills in vector spaces.

charmedbeauty
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Homework Statement



for some reason I am having real trouble trying to solve this system.


Homework Equations





The Attempt at a Solution




a=(10,11,4) v1=(2,1,4) v2=(-1,-2,1) v3=(3,3,-1)

the qstn does a belong to the span (v1,v2,v3)?

so I do gauss elim

but I keep running into dead ends can someone please show just the steps to start i.e. R1=R2 +R3

because every time I have tried I can't get the bottom row to have ENOUGH 0'S!

Thanks.
 
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Can you please show your work so that we may see how far you have gone and where you have gotten stuck?
 
I do not see anything special about this system. Show us what goes wrong for you.
 
voko said:
I do not see anything special about this system. Show us what goes wrong for you.

Well as it turns out it was really easy I just kept making mistakes (it was really late at night)
tried it the next morning and I got it fine.
apparently my brain does not work very well when deprived of sleep. Thanks though
 

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