You decompose a 3×3 matrix A into a lower triangular matrix L and upper triangular matrix U such that A=LU . You have l11=2,l22=5,l33=6,u11=3,u22=7,u33=1 . Here, lij denotes the i, j element of L and uij denotes the i, j element of U . What is the determinant of A ?

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

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?

What rotation was applied to triangle def to create d’e’f’?