Consider the linear system 211 + 3x2 - 5.23 = b 7.01 + 2.02 + 813 = b2 -x1 + 12 - 5.23 = b3

(a) find the echelon form of the augmented matrix of the above system.

(b) find the conditions on b1,b2, b3 for which this system has a solution.

(c) do you see the shape of the points (61, 62, 63) for which the above system has a solution?

(d) if you randomly picked a (61, 62, 63) in r3, do you expect the above system to have a solution?

You are in charge of the customer service phone line with many employees. at the end of each phone callthe customers are asked to rate their service from 1 to 5 stars, with 5 being the best. you find the averagerating for 20 randomly selected employees and decide you want to improve the ratings so you require thoseemployees to go through a new training program. you then wait a week and find the new average rating foreach employee. the average change is an increase in 1.3 stars with a standard devation of .9 stars.(a) is this data paired or not paired? (b) what are the null and alternative hypothesis being tested? (c) what is the t-statistic you would use? write the general formula and the final calculation.(d) sketch a t-distribution, label your t-statistic and the probability you would be interested in: