Let a be an m × n matrix. which of the following statements must be true regarding the nullity (dimension of the null space) of a?

i) the nullity of a is the same as the number of nonzero rows in a row echelon form of a.
ii) the nullity of a is the same as the dimension of the column space of a.
iii) the nullity of a is the same as the nullity of a^t

a. none of the statements are correct.
b. i) and ii) only
c. i) and iii) only
d. ii) and iii) only
e. all three statements are correct.

my answer is$ 12

step-by-step explanation:

because 15 -2=12

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

9 x 8 divided by (5-3)=36

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560