2 - 5 - simul eq + planes

Question 1

consistent

Answer 1

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

Question 2

inconsistent

Answer 2

cant solve simul eqs
no solutions

Question 3

non singular

Answer 3

det != 0
unique solution

Question 4

singular

Answer 4

det = 0
either infinitely many or no solutions

Question 5

system of 2 simultaneous eq as matrices

Answer 5

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

Question 6

how 2 planes can be arranged

Answer 6

• intersect in a line
• parallel - normal vectors are multiples

Question 7

3 planes arrangements

Answer 7

• 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

Question 8

system of 3 simul eq

Answer 8

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