Check the statements below that are true.

a. a single vector by itself is linearly dependent.
b. a basis is a spanning set that is as large as possible.
c. the columns of an invertible n×n matrix form a basis for rn.
d. if v=span{v1,}, then {v1,} is a basis for v.
e. in some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.

2people are trying different phones to see which one has the better talk time. chatlong has an average of 18 hours with a standard deviation of 2 hours and talk-a-lot has an average of 20 hours with a standard deviation of 3. the two people who tested their phones both got 20 hours of use on their phones. for the z-scores i got 1 for the chatlong company and 0 for talk-a-lot. what is the percentile for each z-score?