This second programming assignment will require you to write an R function that is able to cache potentially time-consuming computations. For example, taking the mean of a numeric vector is typically a fast operation. However, for a very long vector, it may take too long to compute the mean, especially if it has to be computed repeatedly (e.g. in a loop). If the contents of a vector are not changing, it may make sense to cache the value of the mean so that when we need it again, it can be looked up in the cache rather than recomputed. In this Programming Assignment you will take advantage of the scoping rules of the R language and how they can be manipulated to preserve state inside of an R object.
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.
Write the following functions:
makeCacheMatrix
: This function creates a special "matrix" object that can cache its inverse.cacheSolve
: This function computes the inverse of the special "matrix" returned bymakeCacheMatrix
above. If the inverse has already been calculated (and the matrix has not changed), thencacheSolve
should retrieve the inverse from the cache.
Computing the inverse of a square matrix can be done with the solve
function in R. For example, if X
is a square invertible matrix, then
solve(X)
returns its inverse.
For this assignment, assume that the matrix supplied is always invertible.