Let T be a linear transformation from R^3 to R^3 Determine whether or not T is one-to-one in each of the following situations:.
1. Suppose T(0, -2, -4) = u. T(-3,-4,1) = v. T(-3, -5, -3) = u + v.
2. Suppose T(a) = u, T(b) = v. T(c) = u + v. where a, b,c, u,v v are vectors in R^3
3. Suppose T is an onto function
A. T is not a one-to-one function
B. T is a one-to-one function
C. There is not enough information to tell

Construct the graph that models the given situation

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

The bottom of ignacio's desktop is 74.5cm from the floor. ignacios sits in his adjustable chair, and the tops of his legs are 49.3cm from the floor. each clockwise rotation of the knob on the chair raises ignacio's legs by 4.8cm. write an inequality to determine the number of clockwise rotations, r, ignacio could make with the knob without his legs touching the desk.