Dot Product

Question 1

dot product is

Answer 1

u • v = u1v1 + u2v2 . . . + unvn

scalar number

Question 2

commutativity (of dot product)

Answer 2

u • v = v • u

Question 3

distributivity

Answer 3

u • (v + w)= u • v + u • w

cu) • v = c(u • v) = u • (cv

Question 4

limits of v • v

Answer 4

v • v ≥ 0

v • v = 0 if and only if v=0

Question 5

how do you prove a for all statement

Answer 5

use general terms and values to show that the if part is true no matter what the values are
No specific examples can prove it

Question 6

how do you disprove a for all statement

Answer 6

you use a specific counterexample where the if is true but the then is false. Can use specific values because if even one case that statement is false, then it has been disproven