You may use MATLAB to manipulate matrices. You do not need to show that work; just specify places where this was done in you write-up. A square matrix is said to be doubly stochastic if the sum of the entries in each column is 1 and the sum of the entries in each row is 1. Some examples of doubly stochastic matrices are .1 .2 .3 41 4 .6 6 .4 13 .6 6 1 3d .3 4 1 1. Give another example of a 2 x 2 doubly stochastic matrix. (a). is your matrix symmetric? That is, does it equal its own transpose? (b). Prove that every 2 x 2 doubly stochastic matrix is symmetric. (c). Show that the product of your matrix and the matrix 4 .6 6 1 is doubly stochastic. (d). Show that a stable distribution for your matrix 2. Give another example of a 3 x 3 doubly stochastic matrix (a). Is your matrix symmetric? Are all 3 x 3 doubly stochastic matrices symmetric? (b). Show that the product of your matrix and the matrix 2 3 6 1 is doubly stochastic