## Here is an overall description of my two functions:

## 1. makeCacheMatrix

## 2. cacheSolve

## Below I have written in more detail about these two functions. At the end

## I have added an example.

## Regarding 1. MakeCacheMatrix.

## Write a short comment describing this function

## The input for makeCacheMatrix is a matrix type and do the following:

## 1. set the value of the matrix

## 2. get the value of matrix

## 3. set value of the inverse of the matrix

## 4. get value of the inverse of matrix

## in the program(MakeCacheMatrix) i have put 1-4(as a comment),where this is done

makeCacheMatrix <- function(x = matrix()) {

## Set the mean to NULL (1)

m <- NULL

## The set function defines a new funtion that set the matrix x to a new matrix y

## and resets the inverse m to NULL (1).

## I have used `<<-` to assign a value to an object in an environment

## different from the current environment.

set <- function(y) {

x <<- y

m <<- NULL

}

## The get function returns the matrix x (2)

get <- function() x

## The setsolve function assign solve to m (3)

setsolve <- function(solve) m <<- solve

## The getsolve returns the inverse value m (4)

getsolve <- function() m

## The list command returns the vector of values of the functions just defined

## This list is an object that will be called from the cacheSolve function below

list(set = set, get = get,

setsolve = setsolve,

getsolve = getsolve)

}

## Regarding 2. cacheSolve.

## This function returns the inverse of (A^-1) if the matrix has not changed

## then it will return the cached value otherwise it re-calculates the inverse.

##

cacheSolve <- function(x, ...) {

## Return a matrix that is the inverse of 'x'

m <- x$getsolve() ## assigns the value of x$getsolve to m

if(!is.null(m)) {

## !is.null(m) return FALSE if it is argument is null and TRUE otherwise

## if true it prints the messages and return the cached value m

message("getting cached data")

return(m)

}

## In the case that the above if statement is FALSE:

data <- x$get() ## get the value x$get() and assigns it to data

m <- solve(data, ...) ## calculate the inverse matrix of data and assigns it to m

x$setsolve(m) ## Sets the value of the inverse in cache with the setsolve function

m ## Return the inverse matrix

}

## Try the following experiment:

## v<-matrix(1:4,2,2)

## s<-makeCacheMatrix(v)

## cacheSolve(s)

## [,1] [,2]

## [1,] -2 1.5

## [2,] 1 -0.5

## cacheSolve(s)

## getting cached data

## [,1] [,2]

## [1,] -2 1.5

## [2,] 1 -0.5