this is the code from my complete R file.

## In this assignments, there are 2 functions. The first one creates a special “matrix” object that can cache its inverse;

## the second one computes the inverse of the special "matrix" returned by makeCacheMatrix. If the inverse has already been calculated

## (and the matrix has not changed), then the cachesolve should retrieve the inverse from the cache.

## Write a short comment describing the first function 'makeCacheMatrix'

## MakeCacheMatrix:this function creates a special “matrix” object that can cache its inverse.

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

cacheMatrix <- NULL # assign NULL to an object cacheMatrix

set <- function(y) { # assign a value to an objects in an environment

# that is different from the current environment

x <<- y

cacheMatrix <<- NULL

}

get <- function() x # this function get the value of the matrix

setsolve <- function(solve) cacheMatrix <<- solve #this function set

#the value of the inverse matrix in the cache

getsolve <- function() cacheMatrix # this function get the value of the

# inverse matrix from the cache

list(set = set, get = get,

setsolve = setsolve,

getsolve = getsolve)

}

## Write a short comment describing the second function 'cacheSolve'

## cacheSolve: this function computes the inverse of the special "matrix" returned by makeCacheMatrix.

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

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

cacheMatrix <- x$getsolve()

if(!is.null(cacheMatrix)) { # checks to see if the inverse matrix has

# already been calculated.If so, it gets the

# value from the cache and return it.

message("getting cached data")

return(cacheMatrix)

}

data <- x$get() # this portion calculates the inverse of the matrix and sets the value in the cache via the setmean function

cacheMatrix <- solve(data, ...)

x$setSolve(cacheMatrix)

cacheMatrix

}