<prompt> Ho latela matrix a phetoho, bala kabo e emengPhetoho ea matrix: 0.7, 0.3, 0.3, 0.7  <response>: Instruction in English: Given a transition matrix, calculate the stationary distribution . Response in English: A stationary distribution of a Markov chain is a probability distribution that remains unchanged in the Markov chain as time progresses. In other words, its a vector of probabilities that satisfies the equation pi pi P, where pi is the stationary distribution and P is the transition matrix.To find the stationary distribution for the given transition matrix, we can follow these steps:1. First, lets construct the system of equations using the matrix equation piP pi:0.7pi0 0.3pi1 - pi0 00.3pi0 0.7pi1 - pi1 0These can be simplified to:-0.3pi0 0.3pi1 00.3pi0 - 0.3pi1 02. Solving these equations, we find that pi0 pi1.Since the probabilities must sum up to 1, this means that pi0 pi1 12.Therefore, the stationary distribution for the given transition matrix is 12, 12. . Response in Sesotho: Kabo e emeng ea ketane ea Markov ke kabo ea monyetla e lulang e sa fetohe ho ketane ea Markov ha nako e ntse e tsoela pele. Ka mantsoe a mang, ke vector ea menyetla e khotsofatsang equation pi pi P, moo pi e leng kabo e emeng le P ke matrix a phetoho. Ho fumana kabo e emeng bakeng sa matrix a phetoho e fanoeng, re ka latela mehato ena: 1. Pele, ha re theheng sistimi ea lipalo re sebelisa matrix equation piP pi: 0.7pi0 0.3pi1 - pi0 0 0.3pi0 0.7pi1 - pi1 0 Tsena li ka nolofatsoa ho: -0.3pi0 0.3pi1 0 0.3pi0 - 0.3pi1 0 2. Ho rarolla lipalo tsena, re fumana hore pi0 pi1. Kaha menyetla e tlameha ho akaretsa ho fihla ho 1, sena se bolela hore pi0 pi1 12. Ka hona, kabo e emeng bakeng sa matrix a phetoho e fanoeng ke 12, 12. 