2 - 5 - simul eq + planes Flashcards

1
Q

consistent

A

simul eq can be solved to a point or are multiples of each other
has a solution/ infinitely many solutions

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2
Q

inconsistent

A

cant solve simul eqs
no solutions

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3
Q

non singular

A

det != 0
unique solution

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4
Q

singular

A

det = 0
either infinitely many or no solutions

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5
Q

system of 2 simultaneous eq as matrices

A

if det != 0
- unique solution
if det = 0
- no unique solution
- - if consistent - infinite solutions
- - if inconsistent - no solutions

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6
Q

how 2 planes can be arranged

A
  • intersect in a line
  • parallel - normal vectors are multiples
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7
Q

3 planes arrangements

A
  • meet at a point - consistent - unique sol
  • meet in a line - consistent - infinite sol (sheaf)
  • all 3 parallel - inconsistent - no sol
  • 2 parallel one intersects - inconsistent - no sol
  • triangular prism - inconsistent - no sol
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8
Q

system of 3 simul eq

A

if det != 0
- unique solution - meet at a point
if det = 0
- no unique solution
- - if consistent - infinite solutions - meet at a line - sheaf
- - if inconsistent - no solutions - parallel or prism

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9
Q
A
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