Caching the Inverse of a Matrix:

Matrix inversion is usually a costly computation and there may be some

benefit to caching the inverse of a matrix rather than compute it repeatedly.

Below are a pair of functions that are used to create a special object that

stores a matrix and caches its inverse.

This function creates a special "matrix" object that can cache its inverse.

makeCacheMatrix <- function(x = matrix()) {
inv <- NULL
set <- function(y) {
x <<- y
inv <<- NULL
}
get <- function() x
setInverse <- function(inverse) inv <<- inverse
getInverse <- function() inv
list(set = set,
get = get,
setInverse = setInverse,
getInverse = getInverse)
}

This function computes the inverse of the special "matrix" created by

makeCacheMatrix above. If the inverse has already been calculated (and the

matrix has not changed), then it should retrieve the inverse from the cache.

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

Return a matrix that is the inverse of 'x'

inv <- x$getInverse()
if (!is.null(inv)) {
message("getting cached data")
return(inv)
}
mat <- x$get()
inv <- solve(mat, ...)
x$setInverse(inv)
inv
}

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Caching the Inverse of a Matrix:
Matrix inversion is usually a time taking activity and there may be some
the benefit to caching the inverse of a matrix rather than compute it repeatedly. pair of functions that are used to create a special object that stores a matrix and caches its inverse.
This function creates a special "matrix" object.

makeCacheMatrix <- function(x = matrix()){
inv <- NULL
set <- function(y){
x <<- y
inv <<- NULL
}
get <- function() {x}
SetInverse <- function(inverse) {inv <<- inverse}
getInverse <- function() {inv}
list(set = set, get = get, setInverse = setInverse, getInverse = getInverse)
}

The following function returns the inverse of cache matrix. And evaluates the inverse of a matrix

cacheSolve <- function(x, ...){
inv <- x$getInverse()
if(!is.null(inv)){
message("getting cached data")
return(inv)
}
mat <- x$get()
inv <- solve(mat, ...)
x$setInverse(inv)
inv
}

please review the assignment

Put comments here that give an overall description of what your

functions do

Write a short comment describing this function

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

}

Write a short comment describing this function

cacheSolve <- function(x, ...) {
## Return a matrix that is the inverse of 'x'
}

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Programming Assignment II

	### Creat Special Matrix

makeCacheMatrix <- function(x = matrix()) {
j <- NULL
set <- function(y){
x <<- y ### Assignment Operator in the Parent Environment
j <<- NULL
}
get <- function()x
setInverse <- function(inverse) j <<- inverse
getInverse <- function() j
list(set = set, get = get,
setInverse = setInverse,
getInverse = getInverse)
}
### Cache the Matrix
cacheSolve <- function(x, ...) {
### Return a matrix that is the inverse of 'x'
j <- x$getInverse()
if(!is.null(j)){
message("getting cached data")
return(j)
}
mat <- x$get()
j <- solve(mat,...)
x$setInverse(j)
j
}

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