show all work) In a certain town, it haeen observed that · if a day is sunny, then 4 out of 5 times it is followed by a sunny day, · if a day is cloudy, then it has 70% chance of being followed by another cloudy one. a. Let S® and C) represent the probability of the ith day being sunny or cloudy, respectively. Find the 2 × 2 matrix A such that [S(i+1)] = A b. Show that A is a regular matrix. c. Show that Ais a stochastic matrix. d. Starting with a sunny day, calculate the probability vectors i = 1,2,3. Repeat this calculation starting with a cloudy day instead. e. Find the stable vector of A and compare it to the vectors obtained in for part (d).

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.