Math 210-01: Linear Algebra: Reading Homework 2.5

1. Applications of Matrix Operations :
   
   1. Stochastic Matrices : what do we mean by ``states''? what is a matrix of transition probabilities? under what circumstances is a matrix called ``stochastic''?
      
      1. example : how does the transition probability matrix in example 2 reflect the situation being modeled? how is the matrix related to the state matrices for future years?
         
      2. steady state : what is a steady state? how is it arrived at?
         
   2. Cryptography : what is a cryptogram?
      
      1. uncoded row matrices : what is an uncoded row matrix? why is the name appropriate?
         
      2. coding : how is the message in uncoded row matrix format encoded? how are the coded row matrices turned into the cryptogram?
         
      3. decoding : explain how an inverse matrix is involved with decoding an encoded message
         
   3. Leontief Input-Output Models : what does an input-output matrix in a Leontief input-output model relate? how is the total output of a given industry represented?
      
   4. Least-Squares Regression : how can how well a function fits a set of points be measured? what is a least-squares regression line?
      
      1. least-squares linear regression : what system of linear equations appears in the determination of a least squares regression line? what formula gives the coefficients of the line?