linear algebra

(please use a left stochastic matrices (columns add to 1)

1.Suppose that in a different city "Finn's" opens a new studio, and this studio offers a "Lifetime" package.The "Lifetime" package means that once a family buys this package, they are permanently in this "state".Market research shows that the only families that will buy the "Lifetime" package are ones that bought the deluxe package the year before, but only 5% of them. Research also shows that this is a tougher market than the first one.If a family did not purchase a portrait package last year, then there is an 11% chance that they will buy a regular package, and a 5% chance that they will buy a deluxe package. If a family purchased a regular package last year, then there is a 53% chance that they will not purchase a package this year, but a 13% chance that they will buy a deluxe package. If a family purchased a deluxe package last year, there is a 23% chance that they will not buy a package this year, a 31% chance that they will buy a standard package, and we already mentioned that there is a 5% chance that they will buy the "Lifetime" package.

(a)Construct a matrix of transition probabilities for this scenario.