TOPIC: MARKOV CHAINS A market research firm conducted a household survey regarding preferences for three brands of detergents. three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months. consecutive months. The results of the survey are as follows:

Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand. for the "Clean" brand. A) With the above data, write a transition probability matrix and indicate how many housewives were loyal to each brand during that period.