Assignment: 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 computing it repeatedly (there are also alternatives to matrix inversion that we will not discuss here). Your assignment is to write a pair of functions that cache the inverse of a matrix.

The following functions are for evaluation:

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 cacheSolve should retrieve the inverse from the cache.

The following function sets and gets the inverse of the matrix.

    makeCacheMatrix <- function(x = matrix()) {
      m <- NULL
      set <- function(y) {
        x <<- y
        m <<- NULL
      }
      get <- function() x
      setInverseVector <- function(solve) m <<- solve
      getInverseVector <- function() m
      list(set = set, get = get,
           setInverseVector = setInverseVector,
           getInverseVector = getInverseVector)   
    }

The following function Caches the inverse of the matrix from the above function.

cacheSolve <- function(x, ...) {
  m <- x$getInverseVector()
  if(!is.null(m)) {
    message("Getting cached data")
    return(m)
  }
  data <- x$get()
  m <- solve(data, ...)
  x$setInverseVector(m)
  m
  
}

Test Cases to test the cache functions.

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