A Let A Find A Diagonal Matrix D So That P 1ap D For Some Invertible Matrix P You Do Not Need To Find The M 1 (50.92 KiB) Viewed 42 times
A Let A Find A Diagonal Matrix D So That P 1ap D For Some Invertible Matrix P You Do Not Need To Find The M 2 (9.19 KiB) Viewed 42 times
(a) Let = [] A = Find a diagonal matrix D so that P-1AP = D, for some invertible matrix P. You do not need to find the matrix P. (b) A Markov chain is being used to model the daily transport habits of 4000 students. It has two states State 1: travels by train State 2: travels by bus and its transition matrix is P = [1/2 3/10] 1/2 7/10] (i) If 3000 students travel by train initially (day 0), how many of these switch to travelling by bus on day 1? 3/8 (ii) Let x = 5/8 (SSPV), and explain why x is the unique SSPV. (iii) In the long run, how many students travel by bus? (c) Let V1, V2, V3 be any three lineany independent vectors in R³. Show that x is a steady-state probability vector
(c) Let V₁, V2, V3 be any three linearly independent vectors in R³. Determine whether the vectors V₁ + V₂ and v₁ +V₂ +V3 are linearly independent, and justify your answer.
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