Linear Algebra Question - Two Planes

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SUMMARY

The discussion centers on the geometric properties of two planes in linear algebra, specifically addressing the misconception that two planes can intersect at a single point or along an edge. It is established that planes are infinite in extent and do not possess edges, thus they cannot have just one solution. The conversation highlights the challenges of visual representation in mathematics, particularly in diagrams that may imply boundaries where none exist.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly plane equations.
  • Familiarity with geometric interpretations of mathematical constructs.
  • Knowledge of infinite sets and their properties in mathematics.
  • Ability to analyze mathematical diagrams critically.
NEXT STEPS
  • Study the properties of linear equations in three-dimensional space.
  • Learn about the intersection of planes and their geometric implications.
  • Explore the concept of infinite sets in mathematics.
  • Review techniques for accurately representing mathematical concepts through diagrams.
USEFUL FOR

Students studying linear algebra, educators teaching geometric interpretations, and anyone interested in the visual representation of mathematical concepts.

carlodelmundo
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Homework Statement



http://carlodm.com/images/math1.png

My question is:

Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?
 
Last edited by a moderator:
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carlodelmundo said:

Homework Statement



http://carlodm.com/images/math1.png

My question is:

Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?

What's the 'edge' of a plane? I thought planes were unbounded and didn't have 'edges'?
 
Last edited by a moderator:
Oh. Right. I forgot that went infinite. The darn diagrams make it look like they have edges!
 
carlodelmundo said:
Oh. Right. I forgot that went infinite. The darn diagrams make it look like they have edges!

Tough to draw a picture of a plane without edges. Try to sympathise with the illustrators and forgive their lapses.
 

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