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
2
Q
inconsistent
A
cant solve simul eqs
no solutions
3
Q
non singular
A
det != 0
unique solution
4
Q
singular
A
det = 0
either infinitely many or no solutions
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
6
Q
how 2 planes can be arranged
A
- intersect in a line
- parallel - normal vectors are multiples
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
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
9
Q
A