Homogeneous linear system question

  • Thread starter loli12
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  • #1
loli12
Hi, i have a question. Hope you guys can help~

Ques: Give a geometric explanation of why a homogeneous linear system consisting of 2 equations in 3 unknowns must have inifinitely many solutions. What are the possible numbers of solutions for a nonhomogeneous 2 x 3 linear system? Give a geometric explanation of your answer.
 

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  • #2
Tide
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Each equation in your set represents a plane in three dimensions. With only two equations the solutions consist of the intersection of those planes (a line)which corresponds to infinitely many points.
 
  • #3
loli12
I got it, Thanks a lot!!!
 
  • #4
arildno
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A bit more care is required:
Each homogenous equation is an equation of the plane WHICH CONTAIN THE ORIGIN!!
Hence, the system has always at least one solution!
This is by no means always true for an inhomogenous system.
(That is, an inhomogenous system may have no solutions at all (a self-contradictory system))
 

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