H Q.4) Show that a mapping 7 : R3 -> R3 defined by T 2r - y + 42 is linear. c - 3y + 2 . Is is one-to-one transformation? . Does the inverse i.e., 7 exist? If so find it . Verify that (by using a coordinate from R') the input of 7 is the output of T-1. 5 marks 1 Q.5) Find the Characteristic equation (CE) for the matrix A = 2 3 3 6 . Show that the matrix satisfies its CE . Using the CE find A3 . Does the inverse of the matrix exists? If so fin A using the CE. Q.6) (a) Find the unknown currents /1, 12 Ja JA, Is Ie from the Electric circuit in Figure 20 41 10 V 20 0 MW 12 20 0 10 V 20 0 Figure 1: Electric Circuit (b) What do you mean by Markov chain or Markov process? Define the transition matrix of the Markov chain. Find the steady-state vector of the transition matrix P = with =