For a certain group of​ states, it was observed that 60​% of the Democratic governors were succeeded by Democrats and 40​% by Republicans.​ Also, 20​% of the Republican governors were succeeded by Democrats and 80​% by Republicans.   ​(a) Set up the 2×2 stochastic matrix with columns and rows labeled D and R that displays these transitions. ​(b) Compute A2 and A3. ​(c) Suppose that all the current governors are Democrats. Assuming that the current trend holds for three​ elections, what percent of the governors will then be​ Democrats?       D R   ​(a) The stochastic matrix is D     nothing nothing       R nothing nothing ​(b) A2=         A3=         ​(c) nothing​% of the governors will be Democrats after three elections.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.