Suppose that the characteristic polynomial of some matrix a is found to be (lambda - 1)(lambda - 3)^3 (lambda - 5)^5 (lambda - 7)^7. what is the dimension of a? what is the determinant of a? is a invertible? how many eigenspaces does a have?

On her way to work, mrs. larsen gets a green light at a certain traffic light only 30% of the time. she wants to find the probability that she will get a green light at this traffic light all five mornings that she travels to work next week. use the following randomly generated list of 200 five-digit numbers to answer the questions and find the probability. select the digits you will use to represent a favorable outcome. how many favorable outcomes are on this list? what are they? given this simulation, what is the probability that mrs. larsen will get a green light at this traffic light all five mornings next week?