Consider a descrete time

Use the matrices below to perform the indicated operation: ABC. -2 0 9 1/2 3 0 1 0 1 A= 1 8 -3 8= -4 1 6 0= 0 1 1/2 4 5 8 7 -2 10 1[1] A Gaussian cube of edge length 1.0 m is located in the xyz space, as shown in the following figure. If the electric field in this space is expressed as: E = 4x ax + 3(yz + 3)ay V/m Determine: a) The electric flux through the top face of the Gaussian cube b) The net charge enclosed by the Gaussian cube Gaussian surface 1- 20m x- 30 m4. Consider a discrete-time Markov chain with the following probability transition matrix 0 0 P= I-T- VVO 0 0 1 Is it possible to choose values for ar and y so that the Markov chain has the following properties? In each case, state the values of a and y, or give a brief reason why it is not possible. (a) The Markov chain has period 2. (b) The Markov chain is reducible. UNNN (c) The Markov chain has at least one transient state. (d) The Markov chain has invariant distribution (1/4, 1/4, 1/4, 1/4).A stationary distribution of an m-state Markov chain is a probability vector q such that = q P, where P is the probability transition matrix. A Markov chain can have more than one stationary distribution. Identify all the stationary distributions that you can, for the 3-state Markov chain with transition probability matrix O O P Owl Does this Markov chain have a steady-state probability distribution ? 15 points