Check the true statements below:

a. a number c is an eigenvalue of a if and only if the equation (a−ci)x=0 has a nontrivial solution x.
b. finding an eigenvector of a might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
c. to find the eigenvalues of a, reduce a to echelon form.
d. a matrix a is not invertible if and only if 0 is an eigenvalue of a.
e. if ax=λx for some vector x, then λ is an eigenvalue of a.

What dimensions can créate more than one triangle ?

Which graph has figures that can undergo a similarity transformation to justify that they are similar? (obviously not the third one)

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?