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This second programming assignment will require you to write an R function is able to cache potentially time-consuming computations. If the contents of a matrix are not changing, it may make sense to cache the value of the inverse so that when we need it again, it can be looked up in the cache rather than recomputed.

Below are two functions that are used to create a special object that stores a matrix and cache's its inverse.

The first function, makeCacheMatrix creates a special "matrix"", which is really a list containing a function to

1. set the contents of the matrix
2. get the contents of the matrix
3. set the contents of the inverse matrix
4. get the contents of the inverse matrix

makeCacheMatrix <- function() {
        # not shown
}

The following function calculates the inverse of the special "matrix" created with the above function. However, it first checks to see if the inverse has already been calculated. If so, it gets the inverse matrix from the cache and skips the computation. Otherwise, it calculates the inverse of the matrix and stores the inverted matrix in the cache via the setinverse function.

cacheSolve <- function(x, ...) {
        # not shown
}

Matrix inversion is usually a costly computation and their may be some benefit to caching the inverse of a matrix rather than compute it repeatedly.

The script provides the following functions:

1. makeCacheMatrix: This function creates a special "matrix" object that can cache its inverse.
2. cacheSolve: This function computes the inverse of the special "matrix" returned by makeCacheMatrix above. If the inverse has already been calculated and the matrix has not changed, then the cacheSolve should retrieve the inverse from the cache.

Computing the inverse of a square matrix can only be performed on a square invertible matrix. The function cacheSolve assumes the matrix supplied is always invertible.

amatrix = makeCacheMatrix(matrix(c(1,2,3,4), nrow=2, ncol=2))
amatrix$get()         # Returns original matrix
cacheSolve(amatrix)   # Computes, caches, and returns    matrix inverse
amatrix$getinverse()  # Returns matrix inverse
cacheSolve(amatrix)   # Returns cached matrix inverse using previously computed matrix inverse

amatrix$set(matrix(c(0,5,99,66), nrow=2, ncol=2)) # Modify existing matrix
cacheSolve(amatrix)   # Computes, caches, and returns new matrix inverse
amatrix$get()         # Returns matrix
amatrix$getinverse()  # Returns matrix inverse