5. Stochastic and Stochastic n-by-n matrices Recall that an n × n matrix A is said to be stochastic if the following conditions are satisfied (a) Entries of A are non negative, that is ai, j ≥ 0 for all 1 ≤ i ≤ n and all 1 ≤ j ≤ n. (b) Each column of A sums to 1, that is Pn i=1 ai, j = 1, for all 1 ≤ j ≤ n. Let S and M be arbitrary stochastic n-by-n matrices. n matrices Recall that an n × n matrix A is said to be stochastic if the following conditions are satisfied

c

step-by-step explanation:

c

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

step-by-step explanation: