Linear Algebra - System of 2 Equations with 3 Variables-possible?

  • Thread starter chrisdapos
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  • #1
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Linear Algebra - System of 2 Equations with 3 Variables--possible?

Homework Statement


Solve: x1-3x2+4x3=-4
3x1-7x2+7x3=-8
-4x1+6x2-x3=7


The Attempt at a Solution


I was able to make it to:
1 -3 4 -4
0 -10 25 -11
0 0 0 0
So the third row goes away, and I am left with:
1 -3 4 -4
0 -10 25 -11
I am pretty sure that cannot be solved, or am I overlooking something? Thank you in advance!!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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It looks like you have a free variable. So you can solve for the other two in terms of it.
 
  • #3
NateTG
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I am pretty sure that cannot be solved, or am I overlooking something? Thank you in advance!!

The solution isn't unique, you can try plugging in a value for [itex]x_1[/itex] and solving the rest.
[tex]x_1=1,2,3,4,5,6....\pi, e,...[/tex]
 
  • #4
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whenever you have more unknowns than equations, you get infinitely many solutions and one or more variables become free varaibles
 
  • #5
NateTG
Science Advisor
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whenever you have more unknowns than equations, you get infinitely many solutions and one or more variables become free varaibles

Sometimes there can still be zero solutions:
[tex]x+y+z=0[/tex]
[tex]x+y+z=1[/tex]
 

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