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.

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.

12 3 4 5 6 7 8 9 10time remaining01: 24: 54which graph represents this system? y=1/2x + 3 y= 3/2x -1

At a pizza shop 70% of the customers order a pizza 25% of the customers order a salad and 15% of the customers order both a pizza and a salad if s customer is chosen at random what is the probability that he or she orders either a pizza or a salad